algebra.algebra.tower ⟷ Mathlib.Algebra.Algebra.Tower

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

@@ -193,14 +193,13 @@ instance (priority := 999) subsemiring (U : Subsemiring S) : IsScalarTower U S A
 #align is_scalar_tower.subsemiring IsScalarTower.subsemiring
 -/
 
-#print IsScalarTower.of_ring_hom /-
+#print IsScalarTower.of_algHom /-
 @[nolint instance_priority]
-instance of_ring_hom {R A B : Type _} [CommSemiring R] [CommSemiring A] [CommSemiring B]
-    [Algebra R A] [Algebra R B] (f : A →ₐ[R] B) :
-    @IsScalarTower R A B _ f.toRingHom.toAlgebra.toSMul _ :=
+instance of_algHom {R A B : Type _} [CommSemiring R] [CommSemiring A] [CommSemiring B] [Algebra R A]
+    [Algebra R B] (f : A →ₐ[R] B) : @IsScalarTower R A B _ f.toRingHom.toAlgebra.toSMul _ :=
   letI := (f : A →+* B).toAlgebra
   of_algebra_map_eq fun x => (f.commutes x).symm
-#align is_scalar_tower.of_ring_hom IsScalarTower.of_ring_hom
+#align is_scalar_tower.of_ring_hom IsScalarTower.of_algHom
 -/
 
 end Semiring

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Anne Baanen
 -/
-import Mathbin.Algebra.Algebra.Equiv
-import Mathbin.LinearAlgebra.Span
+import Algebra.Algebra.Equiv
+import LinearAlgebra.Span
 
 #align_import algebra.algebra.tower from "leanprover-community/mathlib"@"832f7b9162039c28b9361289c8681f155cae758f"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999

@@ -39,7 +39,6 @@ variable [AddCommMonoid M] [Module R M] [Module A M] [IsScalarTower R A M]
 
 variable {A}
 
-#print Algebra.lsmul /-
 /-- The `R`-algebra morphism `A → End (M)` corresponding to the representation of the algebra `A`
 on the `R`-module `M`.
 
@@ -53,8 +52,7 @@ def lsmul : A →ₐ[R] Module.End R M
   map_zero' := LinearMap.ext fun _ => zero_smul A _
   map_add' a b := LinearMap.ext fun _ => add_smul _ _ _
   commutes' r := LinearMap.ext <| algebraMap_smul A r
-#align algebra.lsmul Algebra.lsmul
--/
+#align algebra.lsmul Algebra.lsmulₓ
 
 #print Algebra.lsmul_coe /-
 @[simp]

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Anne Baanen
-
-! This file was ported from Lean 3 source module algebra.algebra.tower
-! leanprover-community/mathlib commit 832f7b9162039c28b9361289c8681f155cae758f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Equiv
 import Mathbin.LinearAlgebra.Span
 
+#align_import algebra.algebra.tower from "leanprover-community/mathlib"@"832f7b9162039c28b9361289c8681f155cae758f"
+
 /-!
 # Towers of algebras
 

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

@@ -42,6 +42,7 @@ variable [AddCommMonoid M] [Module R M] [Module A M] [IsScalarTower R A M]
 
 variable {A}
 
+#print Algebra.lsmul /-
 /-- The `R`-algebra morphism `A → End (M)` corresponding to the representation of the algebra `A`
 on the `R`-module `M`.
 
@@ -56,11 +57,14 @@ def lsmul : A →ₐ[R] Module.End R M
   map_add' a b := LinearMap.ext fun _ => add_smul _ _ _
   commutes' r := LinearMap.ext <| algebraMap_smul A r
 #align algebra.lsmul Algebra.lsmul
+-/
 
+#print Algebra.lsmul_coe /-
 @[simp]
 theorem lsmul_coe (a : A) : (lsmul R M a : M → M) = (· • ·) a :=
   rfl
 #align algebra.lsmul_coe Algebra.lsmul_coe
+-/
 
 end Algebra
 
@@ -74,9 +78,11 @@ variable [SMul R M] [MulAction A M] [IsScalarTower R A M]
 
 variable {R} (A) {M}
 
+#print IsScalarTower.algebraMap_smul /-
 theorem algebraMap_smul (r : R) (x : M) : algebraMap R A r • x = r • x := by
   rw [Algebra.algebraMap_eq_smul_one, smul_assoc, one_smul]
 #align is_scalar_tower.algebra_map_smul IsScalarTower.algebraMap_smul
+-/
 
 end Module
 
@@ -88,10 +94,12 @@ variable [Algebra R S] [Algebra S A] [Algebra S B]
 
 variable {R S A}
 
+#print IsScalarTower.of_algebraMap_eq /-
 theorem of_algebraMap_eq [Algebra R A]
     (h : ∀ x, algebraMap R A x = algebraMap S A (algebraMap R S x)) : IsScalarTower R S A :=
   ⟨fun x y z => by simp_rw [Algebra.smul_def, RingHom.map_mul, mul_assoc, h]⟩
 #align is_scalar_tower.of_algebra_map_eq IsScalarTower.of_algebraMap_eq
+-/
 
 #print IsScalarTower.of_algebraMap_eq' /-
 /-- See note [partially-applied ext lemmas]. -/
@@ -114,9 +122,11 @@ theorem algebraMap_eq : algebraMap R A = (algebraMap S A).comp (algebraMap R S)
 #align is_scalar_tower.algebra_map_eq IsScalarTower.algebraMap_eq
 -/
 
+#print IsScalarTower.algebraMap_apply /-
 theorem algebraMap_apply (x : R) : algebraMap R A x = algebraMap S A (algebraMap R S x) := by
   rw [algebra_map_eq R S A, RingHom.comp_apply]
 #align is_scalar_tower.algebra_map_apply IsScalarTower.algebraMap_apply
+-/
 
 #print IsScalarTower.Algebra.ext /-
 @[ext]
@@ -140,41 +150,53 @@ def toAlgHom : S →ₐ[R] A :=
 #align is_scalar_tower.to_alg_hom IsScalarTower.toAlgHom
 -/
 
+#print IsScalarTower.toAlgHom_apply /-
 theorem toAlgHom_apply (y : S) : toAlgHom R S A y = algebraMap S A y :=
   rfl
 #align is_scalar_tower.to_alg_hom_apply IsScalarTower.toAlgHom_apply
+-/
 
+#print IsScalarTower.coe_toAlgHom /-
 @[simp]
 theorem coe_toAlgHom : ↑(toAlgHom R S A) = algebraMap S A :=
   RingHom.ext fun _ => rfl
 #align is_scalar_tower.coe_to_alg_hom IsScalarTower.coe_toAlgHom
+-/
 
+#print IsScalarTower.coe_toAlgHom' /-
 @[simp]
 theorem coe_toAlgHom' : (toAlgHom R S A : S → A) = algebraMap S A :=
   rfl
 #align is_scalar_tower.coe_to_alg_hom' IsScalarTower.coe_toAlgHom'
+-/
 
 variable {R S A B}
 
+#print AlgHom.map_algebraMap /-
 @[simp]
 theorem AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) : f (algebraMap R A r) = algebraMap R B r :=
   by rw [algebraMap_apply R S A r, f.commutes, ← algebraMap_apply R S B]
 #align alg_hom.map_algebra_map AlgHom.map_algebraMap
+-/
 
 variable (R)
 
+#print AlgHom.comp_algebraMap_of_tower /-
 @[simp]
 theorem AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
     (f : A →+* B).comp (algebraMap R A) = algebraMap R B :=
   RingHom.ext f.map_algebraMap
 #align alg_hom.comp_algebra_map_of_tower AlgHom.comp_algebraMap_of_tower
+-/
 
 variable (R) {S A B}
 
+#print IsScalarTower.subsemiring /-
 -- conflicts with is_scalar_tower.subalgebra
 instance (priority := 999) subsemiring (U : Subsemiring S) : IsScalarTower U S A :=
   of_algebraMap_eq fun x => rfl
 #align is_scalar_tower.subsemiring IsScalarTower.subsemiring
+-/
 
 #print IsScalarTower.of_ring_hom /-
 @[nolint instance_priority]
@@ -216,19 +238,25 @@ def restrictScalars (f : A →ₐ[S] B) : A →ₐ[R] B :=
 #align alg_hom.restrict_scalars AlgHom.restrictScalars
 -/
 
+#print AlgHom.restrictScalars_apply /-
 theorem restrictScalars_apply (f : A →ₐ[S] B) (x : A) : f.restrictScalars R x = f x :=
   rfl
 #align alg_hom.restrict_scalars_apply AlgHom.restrictScalars_apply
+-/
 
+#print AlgHom.coe_restrictScalars /-
 @[simp]
 theorem coe_restrictScalars (f : A →ₐ[S] B) : (f.restrictScalars R : A →+* B) = f :=
   rfl
 #align alg_hom.coe_restrict_scalars AlgHom.coe_restrictScalars
+-/
 
+#print AlgHom.coe_restrictScalars' /-
 @[simp]
 theorem coe_restrictScalars' (f : A →ₐ[S] B) : (restrictScalars R f : A → B) = f :=
   rfl
 #align alg_hom.coe_restrict_scalars' AlgHom.coe_restrictScalars'
+-/
 
 #print AlgHom.restrictScalars_injective /-
 theorem restrictScalars_injective :
@@ -251,19 +279,25 @@ def restrictScalars (f : A ≃ₐ[S] B) : A ≃ₐ[R] B :=
 #align alg_equiv.restrict_scalars AlgEquiv.restrictScalars
 -/
 
+#print AlgEquiv.restrictScalars_apply /-
 theorem restrictScalars_apply (f : A ≃ₐ[S] B) (x : A) : f.restrictScalars R x = f x :=
   rfl
 #align alg_equiv.restrict_scalars_apply AlgEquiv.restrictScalars_apply
+-/
 
+#print AlgEquiv.coe_restrictScalars /-
 @[simp]
 theorem coe_restrictScalars (f : A ≃ₐ[S] B) : (f.restrictScalars R : A ≃+* B) = f :=
   rfl
 #align alg_equiv.coe_restrict_scalars AlgEquiv.coe_restrictScalars
+-/
 
+#print AlgEquiv.coe_restrictScalars' /-
 @[simp]
 theorem coe_restrictScalars' (f : A ≃ₐ[S] B) : (restrictScalars R f : A → B) = f :=
   rfl
 #align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrictScalars'
+-/
 
 #print AlgEquiv.restrictScalars_injective /-
 theorem restrictScalars_injective :
@@ -284,6 +318,7 @@ variable [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M]
 
 variable [Module R M] [Module A M] [IsScalarTower R A M]
 
+#print Submodule.restrictScalars_span /-
 /-- If `A` is an `R`-algebra such that the induced morphism `R →+* A` is surjective, then the
 `R`-module generated by a set `X` equals the `A`-module generated by `X`. -/
 theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X : Set M) :
@@ -294,11 +329,14 @@ theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X :
   obtain ⟨r, rfl⟩ := hsur a
   simpa [algebraMap_smul] using smul_mem _ r hm
 #align submodule.restrict_scalars_span Submodule.restrictScalars_span
+-/
 
+#print Submodule.coe_span_eq_span_of_surjective /-
 theorem coe_span_eq_span_of_surjective (h : Function.Surjective (algebraMap R A)) (s : Set M) :
     (Submodule.span A s : Set M) = Submodule.span R s :=
   congr_arg coe (Submodule.restrictScalars_span R A h s)
 #align submodule.coe_span_eq_span_of_surjective Submodule.coe_span_eq_span_of_surjective
+-/
 
 end Submodule
 
@@ -328,6 +366,7 @@ theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ s
 
 variable [SMulCommClass R S A]
 
+#print Submodule.smul_mem_span_smul /-
 theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R t) : k • x ∈ span R (s • t) :=
   span_induction hx (fun x hx => smul_mem_span_smul_of_mem (hs.symm ▸ mem_top) hx)
@@ -335,7 +374,9 @@ theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S}
     (fun x y ihx ihy => by rw [smul_add]; exact add_mem ihx ihy) fun c x hx =>
     smul_comm c k x ▸ smul_mem _ _ hx
 #align submodule.smul_mem_span_smul Submodule.smul_mem_span_smul
+-/
 
+#print Submodule.smul_mem_span_smul' /-
 theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R (s • t)) : k • x ∈ span R (s • t) :=
   span_induction hx
@@ -346,7 +387,9 @@ theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S
     (fun x y ihx ihy => by rw [smul_add]; exact add_mem ihx ihy) fun c x hx =>
     smul_comm c k x ▸ smul_mem _ _ hx
 #align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'
+-/
 
+#print Submodule.span_smul_of_span_eq_top /-
 theorem span_smul_of_span_eq_top {s : Set S} (hs : span R s = ⊤) (t : Set A) :
     span R (s • t) = (span S t).restrictScalars R :=
   le_antisymm
@@ -357,6 +400,7 @@ theorem span_smul_of_span_eq_top {s : Set S} (hs : span R s = ⊤) (t : Set A) :
     span_induction hp (fun x hx => one_smul S x ▸ smul_mem_span_smul hs (subset_span hx))
       (zero_mem _) (fun _ _ => add_mem) fun k x hx => smul_mem_span_smul' hs hx
 #align submodule.span_smul_of_span_eq_top Submodule.span_smul_of_span_eq_top
+-/
 
 end Module
 
@@ -366,24 +410,30 @@ variable [CommSemiring R] [Semiring S] [AddCommMonoid A]
 
 variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
+#print Submodule.span_algebraMap_image /-
 /-- A variant of `submodule.span_image` for `algebra_map`. -/
 theorem span_algebraMap_image (a : Set R) :
     Submodule.span R (algebraMap R S '' a) = (Submodule.span R a).map (Algebra.linearMap R S) :=
   (Submodule.span_image <| Algebra.linearMap R S).trans rfl
 #align submodule.span_algebra_map_image Submodule.span_algebraMap_image
+-/
 
+#print Submodule.span_algebraMap_image_of_tower /-
 theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring T] [Module R S]
     [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
     Submodule.span R (algebraMap S T '' a) =
       (Submodule.span R a).map ((Algebra.linearMap S T).restrictScalars R) :=
   (Submodule.span_image <| (Algebra.linearMap S T).restrictScalars R).trans rfl
 #align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_tower
+-/
 
+#print Submodule.map_mem_span_algebraMap_image /-
 theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)
     (hx : x ∈ Submodule.span R a) : algebraMap S T x ∈ Submodule.span R (algebraMap S T '' a) := by
   rw [span_algebra_map_image_of_tower, mem_map]; exact ⟨x, hx, rfl⟩
 #align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_image
+-/
 
 end Algebra
 
@@ -399,10 +449,12 @@ variable [CommSemiring R] [Semiring A] [Algebra R A]
 
 variable [AddCommGroup M] [Module A M] [Module R M] [IsScalarTower R A M]
 
+#print Algebra.lsmul_injective /-
 theorem lsmul_injective [NoZeroSMulDivisors A M] {x : A} (hx : x ≠ 0) :
     Function.Injective (lsmul R M x) :=
   smul_right_injective _ hx
 #align algebra.lsmul_injective Algebra.lsmul_injective
+-/
 
 end Algebra
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -140,32 +140,26 @@ def toAlgHom : S →ₐ[R] A :=
 #align is_scalar_tower.to_alg_hom IsScalarTower.toAlgHom
 -/
 
-#print IsScalarTower.toAlgHom_apply /-
 theorem toAlgHom_apply (y : S) : toAlgHom R S A y = algebraMap S A y :=
   rfl
 #align is_scalar_tower.to_alg_hom_apply IsScalarTower.toAlgHom_apply
--/
 
 @[simp]
 theorem coe_toAlgHom : ↑(toAlgHom R S A) = algebraMap S A :=
   RingHom.ext fun _ => rfl
 #align is_scalar_tower.coe_to_alg_hom IsScalarTower.coe_toAlgHom
 
-#print IsScalarTower.coe_toAlgHom' /-
 @[simp]
 theorem coe_toAlgHom' : (toAlgHom R S A : S → A) = algebraMap S A :=
   rfl
 #align is_scalar_tower.coe_to_alg_hom' IsScalarTower.coe_toAlgHom'
--/
 
 variable {R S A B}
 
-#print AlgHom.map_algebraMap /-
 @[simp]
 theorem AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) : f (algebraMap R A r) = algebraMap R B r :=
   by rw [algebraMap_apply R S A r, f.commutes, ← algebraMap_apply R S B]
 #align alg_hom.map_algebra_map AlgHom.map_algebraMap
--/
 
 variable (R)
 
@@ -222,23 +216,19 @@ def restrictScalars (f : A →ₐ[S] B) : A →ₐ[R] B :=
 #align alg_hom.restrict_scalars AlgHom.restrictScalars
 -/
 
-#print AlgHom.restrictScalars_apply /-
 theorem restrictScalars_apply (f : A →ₐ[S] B) (x : A) : f.restrictScalars R x = f x :=
   rfl
 #align alg_hom.restrict_scalars_apply AlgHom.restrictScalars_apply
--/
 
 @[simp]
 theorem coe_restrictScalars (f : A →ₐ[S] B) : (f.restrictScalars R : A →+* B) = f :=
   rfl
 #align alg_hom.coe_restrict_scalars AlgHom.coe_restrictScalars
 
-#print AlgHom.coe_restrictScalars' /-
 @[simp]
 theorem coe_restrictScalars' (f : A →ₐ[S] B) : (restrictScalars R f : A → B) = f :=
   rfl
 #align alg_hom.coe_restrict_scalars' AlgHom.coe_restrictScalars'
--/
 
 #print AlgHom.restrictScalars_injective /-
 theorem restrictScalars_injective :

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

@@ -28,7 +28,7 @@ An important definition is `to_alg_hom R S A`, the canonical `R`-algebra homomor
 -/
 
 
-open Pointwise
+open scoped Pointwise
 
 universe u v w u₁ v₁
 

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

@@ -42,12 +42,6 @@ variable [AddCommMonoid M] [Module R M] [Module A M] [IsScalarTower R A M]
 
 variable {A}
 
-/- warning: algebra.lsmul -> Algebra.lsmul is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)
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-Case conversion may be inaccurate. Consider using '#align algebra.lsmul Algebra.lsmulₓ'. -/
 /-- The `R`-algebra morphism `A → End (M)` corresponding to the representation of the algebra `A`
 on the `R`-module `M`.
 
@@ -63,9 +57,6 @@ def lsmul : A →ₐ[R] Module.End R M
   commutes' r := LinearMap.ext <| algebraMap_smul A r
 #align algebra.lsmul Algebra.lsmul
 
-/- warning: algebra.lsmul_coe -> Algebra.lsmul_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.lsmul_coe Algebra.lsmul_coeₓ'. -/
 @[simp]
 theorem lsmul_coe (a : A) : (lsmul R M a : M → M) = (· • ·) a :=
   rfl
@@ -83,9 +74,6 @@ variable [SMul R M] [MulAction A M] [IsScalarTower R A M]
 
 variable {R} (A) {M}
 
-/- warning: is_scalar_tower.algebra_map_smul -> IsScalarTower.algebraMap_smul is a dubious translation:
-<too large>
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 theorem algebraMap_smul (r : R) (x : M) : algebraMap R A r • x = r • x := by
   rw [Algebra.algebraMap_eq_smul_one, smul_assoc, one_smul]
 #align is_scalar_tower.algebra_map_smul IsScalarTower.algebraMap_smul
@@ -100,9 +88,6 @@ variable [Algebra R S] [Algebra S A] [Algebra S B]
 
 variable {R S A}
 
-/- warning: is_scalar_tower.of_algebra_map_eq -> IsScalarTower.of_algebraMap_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower.of_algebra_map_eq IsScalarTower.of_algebraMap_eqₓ'. -/
 theorem of_algebraMap_eq [Algebra R A]
     (h : ∀ x, algebraMap R A x = algebraMap S A (algebraMap R S x)) : IsScalarTower R S A :=
   ⟨fun x y z => by simp_rw [Algebra.smul_def, RingHom.map_mul, mul_assoc, h]⟩
@@ -129,9 +114,6 @@ theorem algebraMap_eq : algebraMap R A = (algebraMap S A).comp (algebraMap R S)
 #align is_scalar_tower.algebra_map_eq IsScalarTower.algebraMap_eq
 -/
 
-/- warning: is_scalar_tower.algebra_map_apply -> IsScalarTower.algebraMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_apply IsScalarTower.algebraMap_applyₓ'. -/
 theorem algebraMap_apply (x : R) : algebraMap R A x = algebraMap S A (algebraMap R S x) := by
   rw [algebra_map_eq R S A, RingHom.comp_apply]
 #align is_scalar_tower.algebra_map_apply IsScalarTower.algebraMap_apply
@@ -164,9 +146,6 @@ theorem toAlgHom_apply (y : S) : toAlgHom R S A y = algebraMap S A y :=
 #align is_scalar_tower.to_alg_hom_apply IsScalarTower.toAlgHom_apply
 -/
 
-/- warning: is_scalar_tower.coe_to_alg_hom -> IsScalarTower.coe_toAlgHom is a dubious translation:
-<too large>
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 @[simp]
 theorem coe_toAlgHom : ↑(toAlgHom R S A) = algebraMap S A :=
   RingHom.ext fun _ => rfl
@@ -190,9 +169,6 @@ theorem AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) : f (algebraMap R A r)
 
 variable (R)
 
-/- warning: alg_hom.comp_algebra_map_of_tower -> AlgHom.comp_algebraMap_of_tower is a dubious translation:
-<too large>
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 @[simp]
 theorem AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
     (f : A →+* B).comp (algebraMap R A) = algebraMap R B :=
@@ -201,12 +177,6 @@ theorem AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
 
 variable (R) {S A B}
 
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 -- conflicts with is_scalar_tower.subalgebra
 instance (priority := 999) subsemiring (U : Subsemiring S) : IsScalarTower U S A :=
   of_algebraMap_eq fun x => rfl
@@ -258,9 +228,6 @@ theorem restrictScalars_apply (f : A →ₐ[S] B) (x : A) : f.restrictScalars R
 #align alg_hom.restrict_scalars_apply AlgHom.restrictScalars_apply
 -/
 
-/- warning: alg_hom.coe_restrict_scalars -> AlgHom.coe_restrictScalars is a dubious translation:
-<too large>
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 @[simp]
 theorem coe_restrictScalars (f : A →ₐ[S] B) : (f.restrictScalars R : A →+* B) = f :=
   rfl
@@ -294,24 +261,15 @@ def restrictScalars (f : A ≃ₐ[S] B) : A ≃ₐ[R] B :=
 #align alg_equiv.restrict_scalars AlgEquiv.restrictScalars
 -/
 
-/- warning: alg_equiv.restrict_scalars_apply -> AlgEquiv.restrictScalars_apply is a dubious translation:
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 theorem restrictScalars_apply (f : A ≃ₐ[S] B) (x : A) : f.restrictScalars R x = f x :=
   rfl
 #align alg_equiv.restrict_scalars_apply AlgEquiv.restrictScalars_apply
 
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 @[simp]
 theorem coe_restrictScalars (f : A ≃ₐ[S] B) : (f.restrictScalars R : A ≃+* B) = f :=
   rfl
 #align alg_equiv.coe_restrict_scalars AlgEquiv.coe_restrictScalars
 
-/- warning: alg_equiv.coe_restrict_scalars' -> AlgEquiv.coe_restrictScalars' is a dubious translation:
-<too large>
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 @[simp]
 theorem coe_restrictScalars' (f : A ≃ₐ[S] B) : (restrictScalars R f : A → B) = f :=
   rfl
@@ -336,12 +294,6 @@ variable [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M]
 
 variable [Module R M] [Module A M] [IsScalarTower R A M]
 
-/- warning: submodule.restrict_scalars_span -> Submodule.restrictScalars_span is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M 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-Case conversion may be inaccurate. Consider using '#align submodule.restrict_scalars_span Submodule.restrictScalars_spanₓ'. -/
 /-- If `A` is an `R`-algebra such that the induced morphism `R →+* A` is surjective, then the
 `R`-module generated by a set `X` equals the `A`-module generated by `X`. -/
 theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X : Set M) :
@@ -353,12 +305,6 @@ theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X :
   simpa [algebraMap_smul] using smul_mem _ r hm
 #align submodule.restrict_scalars_span Submodule.restrictScalars_span
 
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 theorem coe_span_eq_span_of_surjective (h : Function.Surjective (algebraMap R A)) (s : Set M) :
     (Submodule.span A s : Set M) = Submodule.span R s :=
   congr_arg coe (Submodule.restrictScalars_span R A h s)
@@ -392,9 +338,6 @@ theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ s
 
 variable [SMulCommClass R S A]
 
-/- warning: submodule.smul_mem_span_smul -> Submodule.smul_mem_span_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul Submodule.smul_mem_span_smulₓ'. -/
 theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R t) : k • x ∈ span R (s • t) :=
   span_induction hx (fun x hx => smul_mem_span_smul_of_mem (hs.symm ▸ mem_top) hx)
@@ -403,9 +346,6 @@ theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S}
     smul_comm c k x ▸ smul_mem _ _ hx
 #align submodule.smul_mem_span_smul Submodule.smul_mem_span_smul
 
-/- warning: submodule.smul_mem_span_smul' -> Submodule.smul_mem_span_smul' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'ₓ'. -/
 theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R (s • t)) : k • x ∈ span R (s • t) :=
   span_induction hx
@@ -417,9 +357,6 @@ theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S
     smul_comm c k x ▸ smul_mem _ _ hx
 #align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'
 
-/- warning: submodule.span_smul_of_span_eq_top -> Submodule.span_smul_of_span_eq_top is a dubious translation:
-<too large>
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 theorem span_smul_of_span_eq_top {s : Set S} (hs : span R s = ⊤) (t : Set A) :
     span R (s • t) = (span S t).restrictScalars R :=
   le_antisymm
@@ -439,21 +376,12 @@ variable [CommSemiring R] [Semiring S] [AddCommMonoid A]
 
 variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
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-Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image Submodule.span_algebraMap_imageₓ'. -/
 /-- A variant of `submodule.span_image` for `algebra_map`. -/
 theorem span_algebraMap_image (a : Set R) :
     Submodule.span R (algebraMap R S '' a) = (Submodule.span R a).map (Algebra.linearMap R S) :=
   (Submodule.span_image <| Algebra.linearMap R S).trans rfl
 #align submodule.span_algebra_map_image Submodule.span_algebraMap_image
 
-/- warning: submodule.span_algebra_map_image_of_tower -> Submodule.span_algebraMap_image_of_tower is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_towerₓ'. -/
 theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring T] [Module R S]
     [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
     Submodule.span R (algebraMap S T '' a) =
@@ -461,9 +389,6 @@ theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring
   (Submodule.span_image <| (Algebra.linearMap S T).restrictScalars R).trans rfl
 #align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_tower
 
-/- warning: submodule.map_mem_span_algebra_map_image -> Submodule.map_mem_span_algebraMap_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_imageₓ'. -/
 theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)
     (hx : x ∈ Submodule.span R a) : algebraMap S T x ∈ Submodule.span R (algebraMap S T '' a) := by
@@ -484,9 +409,6 @@ variable [CommSemiring R] [Semiring A] [Algebra R A]
 
 variable [AddCommGroup M] [Module A M] [Module R M] [IsScalarTower R A M]
 
-/- warning: algebra.lsmul_injective -> Algebra.lsmul_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.lsmul_injective Algebra.lsmul_injectiveₓ'. -/
 theorem lsmul_injective [NoZeroSMulDivisors A M] {x : A} (hx : x ≠ 0) :
     Function.Injective (lsmul R M x) :=
   smul_right_injective _ hx

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

@@ -384,15 +384,9 @@ open IsScalarTower
 theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ span R s) {x : A}
     (hx : x ∈ t) : k • x ∈ span R (s • t) :=
   span_induction hks (fun c hc => subset_span <| Set.mem_smul.2 ⟨c, x, hc, hx, rfl⟩)
-    (by
-      rw [zero_smul]
-      exact zero_mem _)
-    (fun c₁ c₂ ih₁ ih₂ => by
-      rw [add_smul]
-      exact add_mem ih₁ ih₂)
-    fun b c hc => by
-    rw [IsScalarTower.smul_assoc]
-    exact smul_mem _ _ hc
+    (by rw [zero_smul]; exact zero_mem _)
+    (fun c₁ c₂ ih₁ ih₂ => by rw [add_smul]; exact add_mem ih₁ ih₂) fun b c hc => by
+    rw [IsScalarTower.smul_assoc]; exact smul_mem _ _ hc
 #align submodule.smul_mem_span_smul_of_mem Submodule.smul_mem_span_smul_of_mem
 -/
 
@@ -404,13 +398,9 @@ Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_spa
 theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R t) : k • x ∈ span R (s • t) :=
   span_induction hx (fun x hx => smul_mem_span_smul_of_mem (hs.symm ▸ mem_top) hx)
-    (by
-      rw [smul_zero]
-      exact zero_mem _)
-    (fun x y ihx ihy => by
-      rw [smul_add]
-      exact add_mem ihx ihy)
-    fun c x hx => smul_comm c k x ▸ smul_mem _ _ hx
+    (by rw [smul_zero]; exact zero_mem _)
+    (fun x y ihx ihy => by rw [smul_add]; exact add_mem ihx ihy) fun c x hx =>
+    smul_comm c k x ▸ smul_mem _ _ hx
 #align submodule.smul_mem_span_smul Submodule.smul_mem_span_smul
 
 /- warning: submodule.smul_mem_span_smul' -> Submodule.smul_mem_span_smul' is a dubious translation:
@@ -421,15 +411,10 @@ theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S
   span_induction hx
     (fun x hx => by
       let ⟨p, q, hp, hq, hpq⟩ := Set.mem_smul.1 hx
-      rw [← hpq, smul_smul]
-      exact smul_mem_span_smul_of_mem (hs.symm ▸ mem_top) hq)
-    (by
-      rw [smul_zero]
-      exact zero_mem _)
-    (fun x y ihx ihy => by
-      rw [smul_add]
-      exact add_mem ihx ihy)
-    fun c x hx => smul_comm c k x ▸ smul_mem _ _ hx
+      rw [← hpq, smul_smul]; exact smul_mem_span_smul_of_mem (hs.symm ▸ mem_top) hq)
+    (by rw [smul_zero]; exact zero_mem _)
+    (fun x y ihx ihy => by rw [smul_add]; exact add_mem ihx ihy) fun c x hx =>
+    smul_comm c k x ▸ smul_mem _ _ hx
 #align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'
 
 /- warning: submodule.span_smul_of_span_eq_top -> Submodule.span_smul_of_span_eq_top is a dubious translation:
@@ -481,10 +466,8 @@ theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring
 Case conversion may be inaccurate. Consider using '#align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_imageₓ'. -/
 theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)
-    (hx : x ∈ Submodule.span R a) : algebraMap S T x ∈ Submodule.span R (algebraMap S T '' a) :=
-  by
-  rw [span_algebra_map_image_of_tower, mem_map]
-  exact ⟨x, hx, rfl⟩
+    (hx : x ∈ Submodule.span R a) : algebraMap S T x ∈ Submodule.span R (algebraMap S T '' a) := by
+  rw [span_algebra_map_image_of_tower, mem_map]; exact ⟨x, hx, rfl⟩
 #align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_image
 
 end Algebra

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

@@ -64,10 +64,7 @@ def lsmul : A →ₐ[R] Module.End R M
 #align algebra.lsmul Algebra.lsmul
 
 /- warning: algebra.lsmul_coe -> Algebra.lsmul_coe is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.lsmul_coe Algebra.lsmul_coeₓ'. -/
 @[simp]
 theorem lsmul_coe (a : A) : (lsmul R M a : M → M) = (· • ·) a :=
@@ -87,10 +84,7 @@ variable [SMul R M] [MulAction A M] [IsScalarTower R A M]
 variable {R} (A) {M}
 
 /- warning: is_scalar_tower.algebra_map_smul -> IsScalarTower.algebraMap_smul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_smul IsScalarTower.algebraMap_smulₓ'. -/
 theorem algebraMap_smul (r : R) (x : M) : algebraMap R A r • x = r • x := by
   rw [Algebra.algebraMap_eq_smul_one, smul_assoc, one_smul]
@@ -107,10 +101,7 @@ variable [Algebra R S] [Algebra S A] [Algebra S B]
 variable {R S A}
 
 /- warning: is_scalar_tower.of_algebra_map_eq -> IsScalarTower.of_algebraMap_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.of_algebra_map_eq IsScalarTower.of_algebraMap_eqₓ'. -/
 theorem of_algebraMap_eq [Algebra R A]
     (h : ∀ x, algebraMap R A x = algebraMap S A (algebraMap R S x)) : IsScalarTower R S A :=
@@ -139,10 +130,7 @@ theorem algebraMap_eq : algebraMap R A = (algebraMap S A).comp (algebraMap R S)
 -/
 
 /- warning: is_scalar_tower.algebra_map_apply -> IsScalarTower.algebraMap_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_apply IsScalarTower.algebraMap_applyₓ'. -/
 theorem algebraMap_apply (x : R) : algebraMap R A x = algebraMap S A (algebraMap R S x) := by
   rw [algebra_map_eq R S A, RingHom.comp_apply]
@@ -177,10 +165,7 @@ theorem toAlgHom_apply (y : S) : toAlgHom R S A y = algebraMap S A y :=
 -/
 
 /- warning: is_scalar_tower.coe_to_alg_hom -> IsScalarTower.coe_toAlgHom is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.coe_to_alg_hom IsScalarTower.coe_toAlgHomₓ'. -/
 @[simp]
 theorem coe_toAlgHom : ↑(toAlgHom R S A) = algebraMap S A :=
@@ -206,10 +191,7 @@ theorem AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) : f (algebraMap R A r)
 variable (R)
 
 /- warning: alg_hom.comp_algebra_map_of_tower -> AlgHom.comp_algebraMap_of_tower is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.comp_algebra_map_of_tower AlgHom.comp_algebraMap_of_towerₓ'. -/
 @[simp]
 theorem AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
@@ -277,10 +259,7 @@ theorem restrictScalars_apply (f : A →ₐ[S] B) (x : A) : f.restrictScalars R
 -/
 
 /- warning: alg_hom.coe_restrict_scalars -> AlgHom.coe_restrictScalars is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.coe_restrict_scalars AlgHom.coe_restrictScalarsₓ'. -/
 @[simp]
 theorem coe_restrictScalars (f : A →ₐ[S] B) : (f.restrictScalars R : A →+* B) = f :=
@@ -316,20 +295,14 @@ def restrictScalars (f : A ≃ₐ[S] B) : A ≃ₐ[R] B :=
 -/
 
 /- warning: alg_equiv.restrict_scalars_apply -> AlgEquiv.restrictScalars_apply is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u4} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u1, u3, u4, max u4 u3} R A B (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9) (AlgHomClass.linearMapClass.{u1, u3, u4, max u4 u3} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u2, u4} S B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} S B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} S B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6)) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, u4, max u4 u3} S A B (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7) (AlgHomClass.linearMapClass.{u2, u3, u4, max u4 u3} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)))))) f x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_equiv.restrict_scalars_apply AlgEquiv.restrictScalars_applyₓ'. -/
 theorem restrictScalars_apply (f : A ≃ₐ[S] B) (x : A) : f.restrictScalars R x = f x :=
   rfl
 #align alg_equiv.restrict_scalars_apply AlgEquiv.restrictScalars_apply
 
 /- warning: alg_equiv.coe_restrict_scalars -> AlgEquiv.coe_restrictScalars is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u3) (succ u4)} (RingEquiv.{u3, u4} A B (Distrib.toHasMul.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A 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(Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasMul.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Distrib.toHasAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (RingEquiv.{u3, u4} A B (Distrib.toHasMul.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasMul.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B 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(NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (RingEquiv.hasCoeT.{max u3 u4, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A B (Distrib.toHasMul.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasMul.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Distrib.toHasAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (AlgEquivClass.toRingEquivClass.{max u3 u4, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.algEquivClass.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingEquiv.{u3, u4} A B (Distrib.toHasMul.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasMul.{u4} B 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(Distrib.toHasAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingEquiv.{u3, u4} A B (Distrib.toHasMul.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasMul.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Distrib.toHasAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (RingEquiv.hasCoeT.{max u3 u4, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A B (Distrib.toHasMul.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasMul.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Distrib.toHasAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (AlgEquivClass.toRingEquivClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.algEquivClass.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7))))) f)
-but is expected to have type
-  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u4) (succ u3)} (RingEquiv.{u3, u4} A B (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Distrib.toAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (RingEquivClass.toRingEquiv.{max u4 u3, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A B (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Distrib.toAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Distrib.toAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (AlgEquivClass.toRingEquivClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (RingEquivClass.toRingEquiv.{max u4 u3, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A B (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Distrib.toAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Distrib.toAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (AlgEquivClass.toRingEquivClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_equiv.coe_restrict_scalars AlgEquiv.coe_restrictScalarsₓ'. -/
 @[simp]
 theorem coe_restrictScalars (f : A ≃ₐ[S] B) : (f.restrictScalars R : A ≃+* B) = f :=
@@ -337,10 +310,7 @@ theorem coe_restrictScalars (f : A ≃ₐ[S] B) : (f.restrictScalars R : A ≃+*
 #align alg_equiv.coe_restrict_scalars AlgEquiv.coe_restrictScalars
 
 /- warning: alg_equiv.coe_restrict_scalars' -> AlgEquiv.coe_restrictScalars' is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u3) (succ u4)} ((fun (_x : AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) => A -> B) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (coeFn.{max (succ u3) (succ u4), max 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-but is expected to have type
-  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 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(DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))) (SMulZeroClass.toSMul.{u1, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B 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_inst_3 _inst_4 _inst_8 _inst_9)))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A 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_inst_2 _inst_4 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, u4, max u4 u3} S A B (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7) (AlgHomClass.linearMapClass.{u2, u3, u4, max u4 u3} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)))))) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrictScalars'ₓ'. -/
 @[simp]
 theorem coe_restrictScalars' (f : A ≃ₐ[S] B) : (restrictScalars R f : A → B) = f :=
@@ -429,10 +399,7 @@ theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ s
 variable [SMulCommClass R S A]
 
 /- warning: submodule.smul_mem_span_smul -> Submodule.smul_mem_span_smul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.hasTop.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 t)) -> (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (SMul.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 t)) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul Submodule.smul_mem_span_smulₓ'. -/
 theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R t) : k • x ∈ span R (s • t) :=
@@ -447,10 +414,7 @@ theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S}
 #align submodule.smul_mem_span_smul Submodule.smul_mem_span_smul
 
 /- warning: submodule.smul_mem_span_smul' -> Submodule.smul_mem_span_smul' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.hasTop.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))) -> (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (SMul.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'ₓ'. -/
 theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R (s • t)) : k • x ∈ span R (s • t) :=
@@ -469,10 +433,7 @@ theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S
 #align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'
 
 /- warning: submodule.span_smul_of_span_eq_top -> Submodule.span_smul_of_span_eq_top is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.hasTop.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall (t : Set.{u3} A), Eq.{succ u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t)) (Submodule.restrictScalars.{u1, u2, u3} R S A _inst_2 _inst_3 _inst_1 _inst_6 _inst_5 (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) _inst_7 (Submodule.span.{u2, u3} S A _inst_2 _inst_3 _inst_5 t)))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall (t : Set.{u3} A), Eq.{succ u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t)) (Submodule.restrictScalars.{u1, u2, u3} R S A _inst_2 _inst_3 _inst_1 _inst_6 _inst_5 (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) _inst_7 (Submodule.span.{u2, u3} S A _inst_2 _inst_3 _inst_5 t)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.span_smul_of_span_eq_top Submodule.span_smul_of_span_eq_topₓ'. -/
 theorem span_smul_of_span_eq_top {s : Set S} (hs : span R s = ⊤) (t : Set A) :
     span R (s • t) = (span S t).restrictScalars R :=
@@ -506,10 +467,7 @@ theorem span_algebraMap_image (a : Set R) :
 #align submodule.span_algebra_map_image Submodule.span_algebraMap_image
 
 /- warning: submodule.span_algebra_map_image_of_tower -> Submodule.span_algebraMap_image_of_tower is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Module.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u1, u2, u2} R S S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u2, u3} S T (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13))))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)))))] (a : Set.{u2} S), Eq.{succ u3} (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u3} S 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R 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_inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S 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(AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
-but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S 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(Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S 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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_towerₓ'. -/
 theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring T] [Module R S]
     [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
@@ -519,10 +477,7 @@ theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring
 #align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_tower
 
 /- warning: submodule.map_mem_span_algebra_map_image -> Submodule.map_mem_span_algebraMap_image is a dubious translation:
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(CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) x) (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) T (Submodule.setLike.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_imageₓ'. -/
 theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)
@@ -547,10 +502,7 @@ variable [CommSemiring R] [Semiring A] [Algebra R A]
 variable [AddCommGroup M] [Module A M] [Module R M] [IsScalarTower R A M]
 
 /- warning: algebra.lsmul_injective -> Algebra.lsmul_injective is a dubious translation:
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M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) 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-  forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) -> (Function.Injective.{succ u3, succ u3} M M (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) x) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.lsmul_injective Algebra.lsmul_injectiveₓ'. -/
 theorem lsmul_injective [NoZeroSMulDivisors A M] {x : A} (hx : x ≠ 0) :
     Function.Injective (lsmul R M x) :=

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

@@ -67,7 +67,7 @@ def lsmul : A →ₐ[R] Module.End R M
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] (a : A), Eq.{succ u3} ((fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_4 _inst_4 _inst_5 _inst_5) => M -> M) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (fun (_x : AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) (coeFn.{succ u3, succ u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_4 _inst_4 _inst_5 _inst_5) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_4 _inst_5 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (fun (_x : AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) (SMul.smul.{u2, u3} A M (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) a)
 but is expected to have type
-  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] (a : A), Eq.{succ u3} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) a) (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) a) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_4 _inst_5 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) ((fun (x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 : A) (x._@.Mathlib.Algebra.Algebra.Tower._hyg.255 : M) => HSMul.hSMul.{u2, u3, u3} A M M (instHSMul.{u2, u3} A M (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6))))) x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 x._@.Mathlib.Algebra.Algebra.Tower._hyg.255) a)
+  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] (a : A), Eq.{succ u3} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) a) (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) a) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_4 _inst_5 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) ((fun (x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 : A) (x._@.Mathlib.Algebra.Algebra.Tower._hyg.255 : M) => HSMul.hSMul.{u2, u3, u3} A M M (instHSMul.{u2, u3} A M (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6))))) x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 x._@.Mathlib.Algebra.Algebra.Tower._hyg.255) a)
 Case conversion may be inaccurate. Consider using '#align algebra.lsmul_coe Algebra.lsmul_coeₓ'. -/
 @[simp]
 theorem lsmul_coe (a : A) : (lsmul R M a : M → M) = (· • ·) a :=
@@ -319,7 +319,7 @@ def restrictScalars (f : A ≃ₐ[S] B) : A ≃ₐ[R] B :=
 lean 3 declaration is
   forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (x : A), Eq.{succ u4} B (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (fun (_x : AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) => A -> B) (AlgEquiv.hasCoeToFun.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) => A -> B) (AlgEquiv.hasCoeToFun.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) f x)
 but is expected to have type
-  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (x : A), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))) (SMulZeroClass.toSMul.{u1, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u4} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u1, u3, u4, max u4 u3} R A B (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9) (AlgHomClass.linearMapClass.{u1, u3, u4, max u4 u3} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u2, u4} S B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} S B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} S B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6)) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, u4, max u4 u3} S A B (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7) (AlgHomClass.linearMapClass.{u2, u3, u4, max u4 u3} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)))))) f x)
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (x : A), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))) (SMulZeroClass.toSMul.{u1, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u4} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u1, u3, u4, max u4 u3} R A B (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9) (AlgHomClass.linearMapClass.{u1, u3, u4, max u4 u3} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u2, u4} S B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} S B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} S B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6)) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, u4, max u4 u3} S A B (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7) (AlgHomClass.linearMapClass.{u2, u3, u4, max u4 u3} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)))))) f x)
 Case conversion may be inaccurate. Consider using '#align alg_equiv.restrict_scalars_apply AlgEquiv.restrictScalars_applyₓ'. -/
 theorem restrictScalars_apply (f : A ≃ₐ[S] B) (x : A) : f.restrictScalars R x = f x :=
   rfl
@@ -340,7 +340,7 @@ theorem coe_restrictScalars (f : A ≃ₐ[S] B) : (f.restrictScalars R : A ≃+*
 lean 3 declaration is
   forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u3) (succ u4)} ((fun (_x : AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) => A -> B) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (fun (_x : AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) => A -> B) (AlgEquiv.hasCoeToFun.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) => A -> B) (AlgEquiv.hasCoeToFun.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) f)
 but is expected to have type
-  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u4) (succ u3)} (forall (a : A), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))) (SMulZeroClass.toSMul.{u1, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u4} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u1, u3, u4, max u4 u3} R A B (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9) (AlgHomClass.linearMapClass.{u1, u3, u4, max u4 u3} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u2, u4} S B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} S B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} S B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6)) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, u4, max u4 u3} S A B (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7) (AlgHomClass.linearMapClass.{u2, u3, u4, max u4 u3} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)))))) f)
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u4) (succ u3)} (forall (a : A), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))) (SMulZeroClass.toSMul.{u1, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u4} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u1, u3, u4, max u4 u3} R A B (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9) (AlgHomClass.linearMapClass.{u1, u3, u4, max u4 u3} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u2, u4} S B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} S B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} S B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6)) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, u4, max u4 u3} S A B (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7) (AlgHomClass.linearMapClass.{u2, u3, u4, max u4 u3} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)))))) f)
 Case conversion may be inaccurate. Consider using '#align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrictScalars'ₓ'. -/
 @[simp]
 theorem coe_restrictScalars' (f : A ≃ₐ[S] B) : (restrictScalars R f : A → B) = f :=
@@ -550,7 +550,7 @@ variable [AddCommGroup M] [Module A M] [Module R M] [IsScalarTower R A M]
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) -> (Function.Injective.{succ u3, succ u3} M M (coeFn.{succ u3, succ u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (fun (_x : AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) -> (Function.Injective.{succ u3, succ u3} M M (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) x) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
+  forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) -> (Function.Injective.{succ u3, succ u3} M M (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) x) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 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(AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 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(AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
 Case conversion may be inaccurate. Consider using '#align algebra.lsmul_injective Algebra.lsmul_injectiveₓ'. -/
 theorem lsmul_injective [NoZeroSMulDivisors A M] {x : A} (hx : x ≠ 0) :
     Function.Injective (lsmul R M x) :=

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

@@ -90,7 +90,7 @@ variable {R} (A) {M}
 lean 3 declaration is
   forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (MulAction.toHasSmul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (SMul.smul.{u2, u3} A M (MulAction.toHasSmul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (SMul.smul.{u1, u3} R M _inst_4 r x)
 but is expected to have type
-  forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (HSMul.hSMul.{u2, u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) M M (instHSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) M (MulAction.toSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) M (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_2)) _inst_5)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M _inst_4) r x)
+  forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (HSMul.hSMul.{u2, u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) M M (instHSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) M (MulAction.toSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) M (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_2)) _inst_5)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M _inst_4) r x)
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_smul IsScalarTower.algebraMap_smulₓ'. -/
 theorem algebraMap_smul (r : R) (x : M) : algebraMap R A r • x = r • x := by
   rw [Algebra.algebraMap_eq_smul_one, smul_assoc, one_smul]
@@ -110,7 +110,7 @@ variable {R S A}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3], (forall (x : R), Eq.{succ u3} A (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => S -> A) (RingHom.hasCoeToFun.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))) -> (IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3], (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))) -> (IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8))
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3], (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))) -> (IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8))
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.of_algebra_map_eq IsScalarTower.of_algebraMap_eqₓ'. -/
 theorem of_algebraMap_eq [Algebra R A]
     (h : ∀ x, algebraMap R A x = algebraMap S A (algebraMap R S x)) : IsScalarTower R S A :=
@@ -142,7 +142,7 @@ theorem algebraMap_eq : algebraMap R A = (algebraMap S A).comp (algebraMap R S)
 lean 3 declaration is
   forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] (x : R), Eq.{succ u3} A (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => S -> A) (RingHom.hasCoeToFun.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))
 but is expected to have type
-  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))
+  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_apply IsScalarTower.algebraMap_applyₓ'. -/
 theorem algebraMap_apply (x : R) : algebraMap R A x = algebraMap S A (algebraMap R S x) := by
   rw [algebra_map_eq R S A, RingHom.comp_apply]
@@ -370,7 +370,7 @@ variable [Module R M] [Module A M] [IsScalarTower R A M]
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
 Case conversion may be inaccurate. Consider using '#align submodule.restrict_scalars_span Submodule.restrictScalars_spanₓ'. -/
 /-- If `A` is an `R`-algebra such that the induced morphism `R →+* A` is surjective, then the
 `R`-module generated by a set `X` equals the `A`-module generated by `X`. -/
@@ -387,7 +387,7 @@ theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X :
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.setLike.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.setLike.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.setLike.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.setLike.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.setLike.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.setLike.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_span_eq_span_of_surjective Submodule.coe_span_eq_span_of_surjectiveₓ'. -/
 theorem coe_span_eq_span_of_surjective (h : Function.Surjective (algebraMap R A)) (s : Set M) :
     (Submodule.span A s : Set M) = Submodule.span R s :=
@@ -497,7 +497,7 @@ variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
 Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image Submodule.span_algebraMap_imageₓ'. -/
 /-- A variant of `submodule.span_image` for `algebra_map`. -/
 theorem span_algebraMap_image (a : Set R) :
@@ -509,7 +509,7 @@ theorem span_algebraMap_image (a : Set R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Module.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u1, u2, u2} R S S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u2, u3} S T (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13))))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)))))] (a : Set.{u2} S), Eq.{succ u3} (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u3} S T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.restrictScalars.{u1, u2, u2, u3} R S S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u3, u1, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u1, u3, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toSMul.{u3, u1} R T (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R T (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R T (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (Module.toMulActionWithZero.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u1, u3, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toSMul.{u3, u1} R T (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R T (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R T (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (Module.toMulActionWithZero.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
 Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_towerₓ'. -/
 theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring T] [Module R S]
     [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
@@ -522,7 +522,7 @@ theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u2, u3} S T (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_12))))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)))))] (x : S) (a : Set.{u2} S), (Membership.Mem.{u2, u2} S (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.setLike.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.Mem.{u3, u3} T (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)) T (Submodule.setLike.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u3} S T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_12)) a)))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u3, u2, u1} R S T (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_12) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_11)] (x : S) (a : Set.{u2} S), (Membership.mem.{u2, u2} S (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.setLike.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) x) (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) T (Submodule.setLike.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u3, u2, u1} R S T (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_12) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_11)] (x : S) (a : Set.{u2} S), (Membership.mem.{u2, u2} S (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.setLike.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) x) (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) T (Submodule.setLike.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_imageₓ'. -/
 theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -67,7 +67,7 @@ def lsmul : A →ₐ[R] Module.End R M
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] (a : A), Eq.{succ u3} ((fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_4 _inst_4 _inst_5 _inst_5) => M -> M) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (fun (_x : AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) (coeFn.{succ u3, succ u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_4 _inst_4 _inst_5 _inst_5) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_4 _inst_5 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (fun (_x : AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) (SMul.smul.{u2, u3} A M (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) a)
 but is expected to have type
-  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] (a : A), Eq.{succ u3} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) a) (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) a) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_4 _inst_5 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) ((fun (x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 : A) (x._@.Mathlib.Algebra.Algebra.Tower._hyg.255 : M) => HSMul.hSMul.{u2, u3, u3} A M M (instHSMul.{u2, u3} A M (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6))))) x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 x._@.Mathlib.Algebra.Algebra.Tower._hyg.255) a)
+  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] (a : A), Eq.{succ u3} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) a) (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) a) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_4 _inst_5 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) ((fun (x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 : A) (x._@.Mathlib.Algebra.Algebra.Tower._hyg.255 : M) => HSMul.hSMul.{u2, u3, u3} A M M (instHSMul.{u2, u3} A M (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6))))) x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 x._@.Mathlib.Algebra.Algebra.Tower._hyg.255) a)
 Case conversion may be inaccurate. Consider using '#align algebra.lsmul_coe Algebra.lsmul_coeₓ'. -/
 @[simp]
 theorem lsmul_coe (a : A) : (lsmul R M a : M → M) = (· • ·) a :=
@@ -497,7 +497,7 @@ variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
 Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image Submodule.span_algebraMap_imageₓ'. -/
 /-- A variant of `submodule.span_image` for `algebra_map`. -/
 theorem span_algebraMap_image (a : Set R) :
@@ -509,7 +509,7 @@ theorem span_algebraMap_image (a : Set R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Module.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u1, u2, u2} R S S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u2, u3} S T (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13))))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)))))] (a : Set.{u2} S), Eq.{succ u3} (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u3} S T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.restrictScalars.{u1, u2, u2, u3} R S S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u3, u1, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u1, u3, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toSMul.{u3, u1} R T (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R T (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R T (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (Module.toMulActionWithZero.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u1, u3, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toSMul.{u3, u1} R T (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R T (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R T (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (Module.toMulActionWithZero.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
 Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_towerₓ'. -/
 theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring T] [Module R S]
     [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
@@ -550,7 +550,7 @@ variable [AddCommGroup M] [Module A M] [Module R M] [IsScalarTower R A M]
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) -> (Function.Injective.{succ u3, succ u3} M M (coeFn.{succ u3, succ u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (fun (_x : AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) -> (Function.Injective.{succ u3, succ u3} M M (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) x) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
+  forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) -> (Function.Injective.{succ u3, succ u3} M M (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) x) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 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_inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 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(AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
 Case conversion may be inaccurate. Consider using '#align algebra.lsmul_injective Algebra.lsmul_injectiveₓ'. -/
 theorem lsmul_injective [NoZeroSMulDivisors A M] {x : A} (hx : x ≠ 0) :
     Function.Injective (lsmul R M x) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -199,7 +199,7 @@ variable {R S A B}
 #print AlgHom.map_algebraMap /-
 @[simp]
 theorem AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) : f (algebraMap R A r) = algebraMap R B r :=
-  by rw [algebra_map_apply R S A r, f.commutes, ← algebra_map_apply R S B]
+  by rw [algebraMap_apply R S A r, f.commutes, ← algebraMap_apply R S B]
 #align alg_hom.map_algebra_map AlgHom.map_algebraMap
 -/
 
@@ -264,9 +264,8 @@ namespace AlgHom
 /-- R ⟶ S induces S-Alg ⥤ R-Alg -/
 def restrictScalars (f : A →ₐ[S] B) : A →ₐ[R] B :=
   { (f : A →+* B) with
-    commutes' := fun r =>
-      by
-      rw [algebra_map_apply R S A, algebra_map_apply R S B]
+    commutes' := fun r => by
+      rw [algebraMap_apply R S A, algebraMap_apply R S B]
       exact f.commutes (algebraMap R S r) }
 #align alg_hom.restrict_scalars AlgHom.restrictScalars
 -/
@@ -310,9 +309,8 @@ namespace AlgEquiv
 /-- R ⟶ S induces S-Alg ⥤ R-Alg -/
 def restrictScalars (f : A ≃ₐ[S] B) : A ≃ₐ[R] B :=
   { (f : A ≃+* B) with
-    commutes' := fun r =>
-      by
-      rw [algebra_map_apply R S A, algebra_map_apply R S B]
+    commutes' := fun r => by
+      rw [algebraMap_apply R S A, algebraMap_apply R S B]
       exact f.commutes (algebraMap R S r) }
 #align alg_equiv.restrict_scalars AlgEquiv.restrictScalars
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

@@ -196,27 +196,26 @@ theorem coe_toAlgHom' : (toAlgHom R S A : S → A) = algebraMap S A :=
 
 variable {R S A B}
 
-#print IsScalarTower.AlgHom.map_algebraMap /-
+#print AlgHom.map_algebraMap /-
 @[simp]
-theorem IsScalarTower.AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) :
-    f (algebraMap R A r) = algebraMap R B r := by
-  rw [algebra_map_apply R S A r, f.commutes, ← algebra_map_apply R S B]
-#align alg_hom.map_algebra_map IsScalarTower.AlgHom.map_algebraMap
+theorem AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) : f (algebraMap R A r) = algebraMap R B r :=
+  by rw [algebra_map_apply R S A r, f.commutes, ← algebra_map_apply R S B]
+#align alg_hom.map_algebra_map AlgHom.map_algebraMap
 -/
 
 variable (R)
 
-/- warning: alg_hom.comp_algebra_map_of_tower -> IsScalarTower.AlgHom.comp_algebraMap_of_tower is a dubious translation:
+/- warning: alg_hom.comp_algebra_map_of_tower -> AlgHom.comp_algebraMap_of_tower is a dubious translation:
 lean 3 declaration is
   forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u1) (succ u4)} (RingHom.{u1, u4} R B (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (RingHom.comp.{u1, u3, u4} R A B (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (RingHom.hasCoeT.{max u3 u4, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) (AlgHomClass.toRingHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgHom.algHomClass.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7))))) f) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (algebraMap.{u1, u4} R B _inst_1 _inst_4 _inst_9)
 but is expected to have type
   forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u1) (succ u4)} (RingHom.{u1, u4} R B (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (RingHom.comp.{u1, u3, u4} R A B (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) (RingHomClass.toRingHom.{max u4 u3, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) (AlgHomClass.toRingHomClass.{max u4 u3, u2, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgHom.algHomClass.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)) f) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (algebraMap.{u1, u4} R B _inst_1 _inst_4 _inst_9)
-Case conversion may be inaccurate. Consider using '#align alg_hom.comp_algebra_map_of_tower IsScalarTower.AlgHom.comp_algebraMap_of_towerₓ'. -/
+Case conversion may be inaccurate. Consider using '#align alg_hom.comp_algebra_map_of_tower AlgHom.comp_algebraMap_of_towerₓ'. -/
 @[simp]
-theorem IsScalarTower.AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
+theorem AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
     (f : A →+* B).comp (algebraMap R A) = algebraMap R B :=
   RingHom.ext f.map_algebraMap
-#align alg_hom.comp_algebra_map_of_tower IsScalarTower.AlgHom.comp_algebraMap_of_tower
+#align alg_hom.comp_algebra_map_of_tower AlgHom.comp_algebraMap_of_tower
 
 variable (R) {S A B}
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -187,11 +187,11 @@ theorem coe_toAlgHom : ↑(toAlgHom R S A) = algebraMap S A :=
   RingHom.ext fun _ => rfl
 #align is_scalar_tower.coe_to_alg_hom IsScalarTower.coe_toAlgHom
 
-#print IsScalarTower.coe_to_alg_hom' /-
+#print IsScalarTower.coe_toAlgHom' /-
 @[simp]
-theorem coe_to_alg_hom' : (toAlgHom R S A : S → A) = algebraMap S A :=
+theorem coe_toAlgHom' : (toAlgHom R S A : S → A) = algebraMap S A :=
   rfl
-#align is_scalar_tower.coe_to_alg_hom' IsScalarTower.coe_to_alg_hom'
+#align is_scalar_tower.coe_to_alg_hom' IsScalarTower.coe_toAlgHom'
 -/
 
 variable {R S A B}
@@ -289,11 +289,11 @@ theorem coe_restrictScalars (f : A →ₐ[S] B) : (f.restrictScalars R : A →+*
   rfl
 #align alg_hom.coe_restrict_scalars AlgHom.coe_restrictScalars
 
-#print AlgHom.coe_restrict_scalars' /-
+#print AlgHom.coe_restrictScalars' /-
 @[simp]
-theorem coe_restrict_scalars' (f : A →ₐ[S] B) : (restrictScalars R f : A → B) = f :=
+theorem coe_restrictScalars' (f : A →ₐ[S] B) : (restrictScalars R f : A → B) = f :=
   rfl
-#align alg_hom.coe_restrict_scalars' AlgHom.coe_restrict_scalars'
+#align alg_hom.coe_restrict_scalars' AlgHom.coe_restrictScalars'
 -/
 
 #print AlgHom.restrictScalars_injective /-
@@ -339,16 +339,16 @@ theorem coe_restrictScalars (f : A ≃ₐ[S] B) : (f.restrictScalars R : A ≃+*
   rfl
 #align alg_equiv.coe_restrict_scalars AlgEquiv.coe_restrictScalars
 
-/- warning: alg_equiv.coe_restrict_scalars' -> AlgEquiv.coe_restrict_scalars' is a dubious translation:
+/- warning: alg_equiv.coe_restrict_scalars' -> AlgEquiv.coe_restrictScalars' is a dubious translation:
 lean 3 declaration is
   forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u3) (succ u4)} ((fun (_x : AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) => A -> B) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (fun (_x : AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) => A -> B) (AlgEquiv.hasCoeToFun.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) => A -> B) (AlgEquiv.hasCoeToFun.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) f)
 but is expected to have type
   forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u4) (succ u3)} (forall (a : A), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))) (SMulZeroClass.toSMul.{u1, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u4} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u1, u3, u4, max u4 u3} R A B (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9) (AlgHomClass.linearMapClass.{u1, u3, u4, max u4 u3} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u2, u4} S B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} S B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} S B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6)) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, u4, max u4 u3} S A B (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7) (AlgHomClass.linearMapClass.{u2, u3, u4, max u4 u3} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)))))) f)
-Case conversion may be inaccurate. Consider using '#align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrict_scalars'ₓ'. -/
+Case conversion may be inaccurate. Consider using '#align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrictScalars'ₓ'. -/
 @[simp]
-theorem coe_restrict_scalars' (f : A ≃ₐ[S] B) : (restrictScalars R f : A → B) = f :=
+theorem coe_restrictScalars' (f : A ≃ₐ[S] B) : (restrictScalars R f : A → B) = f :=
   rfl
-#align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrict_scalars'
+#align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrictScalars'
 
 #print AlgEquiv.restrictScalars_injective /-
 theorem restrictScalars_injective :

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

@@ -390,7 +390,7 @@ theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X :
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.setLike.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.setLike.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.instSetLikeSubmodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.setLike.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.setLike.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_span_eq_span_of_surjective Submodule.coe_span_eq_span_of_surjectiveₓ'. -/
 theorem coe_span_eq_span_of_surjective (h : Function.Surjective (algebraMap R A)) (s : Set M) :
     (Submodule.span A s : Set M) = Submodule.span R s :=
@@ -413,12 +413,7 @@ variable [Module R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
 open IsScalarTower
 
-/- warning: submodule.smul_mem_span_smul_of_mem -> Submodule.smul_mem_span_smul_of_mem is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] {s : Set.{u2} S} {t : Set.{u3} A} {k : S}, (Membership.Mem.{u2, u2} S (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) S (Submodule.setLike.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)) k (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s)) -> (forall {x : A}, (Membership.Mem.{u3, u3} A (Set.{u3} A) (Set.hasMem.{u3} A) x t) -> (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (SMul.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] {s : Set.{u2} S} {t : Set.{u3} A} {k : S}, (Membership.mem.{u2, u2} S (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) S (Submodule.instSetLikeSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)) k (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s)) -> (forall {x : A}, (Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x t) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
-Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul_of_mem Submodule.smul_mem_span_smul_of_memₓ'. -/
+#print Submodule.smul_mem_span_smul_of_mem /-
 theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ span R s) {x : A}
     (hx : x ∈ t) : k • x ∈ span R (s • t) :=
   span_induction hks (fun c hc => subset_span <| Set.mem_smul.2 ⟨c, x, hc, hx, rfl⟩)
@@ -432,6 +427,7 @@ theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ s
     rw [IsScalarTower.smul_assoc]
     exact smul_mem _ _ hc
 #align submodule.smul_mem_span_smul_of_mem Submodule.smul_mem_span_smul_of_mem
+-/
 
 variable [SMulCommClass R S A]
 
@@ -439,7 +435,7 @@ variable [SMulCommClass R S A]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.hasTop.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 t)) -> (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (SMul.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 t)) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 t)) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
 Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul Submodule.smul_mem_span_smulₓ'. -/
 theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R t) : k • x ∈ span R (s • t) :=
@@ -457,7 +453,7 @@ theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.hasTop.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))) -> (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (SMul.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
 Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'ₓ'. -/
 theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R (s • t)) : k • x ∈ span R (s • t) :=
@@ -529,7 +525,7 @@ theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u2, u3} S T (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_12))))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)))))] (x : S) (a : Set.{u2} S), (Membership.Mem.{u2, u2} S (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.setLike.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.Mem.{u3, u3} T (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)) T (Submodule.setLike.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u3} S T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_12)) a)))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u3, u2, u1} R S T (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_12) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_11)] (x : S) (a : Set.{u2} S), (Membership.mem.{u2, u2} S (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.instSetLikeSubmodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) x) (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) T (Submodule.instSetLikeSubmodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u3, u2, u1} R S T (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_12) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_11)] (x : S) (a : Set.{u2} S), (Membership.mem.{u2, u2} S (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.setLike.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) x) (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) T (Submodule.setLike.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_imageₓ'. -/
 theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)

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

@@ -67,7 +67,7 @@ def lsmul : A →ₐ[R] Module.End R M
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] (a : A), Eq.{succ u3} ((fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_4 _inst_4 _inst_5 _inst_5) => M -> M) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (fun (_x : AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) (coeFn.{succ u3, succ u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) (SMul.smul.{u2, u3} A M (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) a)
 but is expected to have type
-  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] (a : A), Eq.{succ u3} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M) a) (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) a) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_4 _inst_5 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) ((fun (x._@.Mathlib.Algebra.Algebra.Tower._hyg.251 : A) (x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 : M) => HSMul.hSMul.{u2, u3, u3} A M M (instHSMul.{u2, u3} A M (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6))))) x._@.Mathlib.Algebra.Algebra.Tower._hyg.251 x._@.Mathlib.Algebra.Algebra.Tower._hyg.253) a)
+  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] (a : A), Eq.{succ u3} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) a) (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) a) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_4 _inst_5 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) ((fun (x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 : A) (x._@.Mathlib.Algebra.Algebra.Tower._hyg.255 : M) => HSMul.hSMul.{u2, u3, u3} A M M (instHSMul.{u2, u3} A M (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6))))) x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 x._@.Mathlib.Algebra.Algebra.Tower._hyg.255) a)
 Case conversion may be inaccurate. Consider using '#align algebra.lsmul_coe Algebra.lsmul_coeₓ'. -/
 @[simp]
 theorem lsmul_coe (a : A) : (lsmul R M a : M → M) = (· • ·) a :=
@@ -90,7 +90,7 @@ variable {R} (A) {M}
 lean 3 declaration is
   forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (MulAction.toHasSmul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (SMul.smul.{u2, u3} A M (MulAction.toHasSmul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (SMul.smul.{u1, u3} R M _inst_4 r x)
 but is expected to have type
-  forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (HSMul.hSMul.{u2, u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) M M (instHSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) M (MulAction.toSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) M (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) _inst_2)) _inst_5)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M _inst_4) r x)
+  forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (HSMul.hSMul.{u2, u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) M M (instHSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) M (MulAction.toSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) M (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_2)) _inst_5)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M _inst_4) r x)
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_smul IsScalarTower.algebraMap_smulₓ'. -/
 theorem algebraMap_smul (r : R) (x : M) : algebraMap R A r • x = r • x := by
   rw [Algebra.algebraMap_eq_smul_one, smul_assoc, one_smul]
@@ -110,7 +110,7 @@ variable {R S A}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3], (forall (x : R), Eq.{succ u3} A (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => S -> A) (RingHom.hasCoeToFun.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))) -> (IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3], (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))) -> (IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8))
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3], (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))) -> (IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8))
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.of_algebra_map_eq IsScalarTower.of_algebraMap_eqₓ'. -/
 theorem of_algebraMap_eq [Algebra R A]
     (h : ∀ x, algebraMap R A x = algebraMap S A (algebraMap R S x)) : IsScalarTower R S A :=
@@ -142,7 +142,7 @@ theorem algebraMap_eq : algebraMap R A = (algebraMap S A).comp (algebraMap R S)
 lean 3 declaration is
   forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] (x : R), Eq.{succ u3} A (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => S -> A) (RingHom.hasCoeToFun.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))
 but is expected to have type
-  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))
+  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_apply IsScalarTower.algebraMap_applyₓ'. -/
 theorem algebraMap_apply (x : R) : algebraMap R A x = algebraMap S A (algebraMap R S x) := by
   rw [algebra_map_eq R S A, RingHom.comp_apply]
@@ -373,7 +373,7 @@ variable [Module R M] [Module A M] [IsScalarTower R A M]
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
 Case conversion may be inaccurate. Consider using '#align submodule.restrict_scalars_span Submodule.restrictScalars_spanₓ'. -/
 /-- If `A` is an `R`-algebra such that the induced morphism `R →+* A` is surjective, then the
 `R`-module generated by a set `X` equals the `A`-module generated by `X`. -/
@@ -390,7 +390,7 @@ theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X :
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.setLike.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.setLike.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.instSetLikeSubmodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.instSetLikeSubmodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_span_eq_span_of_surjective Submodule.coe_span_eq_span_of_surjectiveₓ'. -/
 theorem coe_span_eq_span_of_surjective (h : Function.Surjective (algebraMap R A)) (s : Set M) :
     (Submodule.span A s : Set M) = Submodule.span R s :=
@@ -504,7 +504,7 @@ variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
 Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image Submodule.span_algebraMap_imageₓ'. -/
 /-- A variant of `submodule.span_image` for `algebra_map`. -/
 theorem span_algebraMap_image (a : Set R) :
@@ -516,7 +516,7 @@ theorem span_algebraMap_image (a : Set R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Module.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u1, u2, u2} R S S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u2, u3} S T (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13))))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)))))] (a : Set.{u2} S), Eq.{succ u3} (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u3} S T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.restrictScalars.{u1, u2, u2, u3} R S S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u3, u1, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u1, u3, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toSMul.{u3, u1} R T (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R T (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R T (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (Module.toMulActionWithZero.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u1, u3, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toSMul.{u3, u1} R T (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R T (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R T (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (Module.toMulActionWithZero.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
 Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_towerₓ'. -/
 theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring T] [Module R S]
     [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
@@ -529,7 +529,7 @@ theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u2, u3} S T (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_12))))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)))))] (x : S) (a : Set.{u2} S), (Membership.Mem.{u2, u2} S (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.setLike.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.Mem.{u3, u3} T (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)) T (Submodule.setLike.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u3} S T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_12)) a)))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u3, u2, u1} R S T (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_12) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_11)] (x : S) (a : Set.{u2} S), (Membership.mem.{u2, u2} S (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.instSetLikeSubmodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) x) (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) T (Submodule.instSetLikeSubmodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u3, u2, u1} R S T (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_12) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_11)] (x : S) (a : Set.{u2} S), (Membership.mem.{u2, u2} S (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.instSetLikeSubmodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) x) (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) T (Submodule.instSetLikeSubmodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_imageₓ'. -/
 theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)
@@ -557,7 +557,7 @@ variable [AddCommGroup M] [Module A M] [Module R M] [IsScalarTower R A M]
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) -> (Function.Injective.{succ u3, succ u3} M M (coeFn.{succ u3, succ u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (fun (_x : AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) -> (Function.Injective.{succ u3, succ u3} M M (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) x) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
+  forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) -> (Function.Injective.{succ u3, succ u3} M M (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) x) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
 Case conversion may be inaccurate. Consider using '#align algebra.lsmul_injective Algebra.lsmul_injectiveₓ'. -/
 theorem lsmul_injective [NoZeroSMulDivisors A M] {x : A} (hx : x ≠ 0) :
     Function.Injective (lsmul R M x) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -90,7 +90,7 @@ variable {R} (A) {M}
 lean 3 declaration is
   forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (MulAction.toHasSmul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (SMul.smul.{u2, u3} A M (MulAction.toHasSmul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (SMul.smul.{u1, u3} R M _inst_4 r x)
 but is expected to have type
-  forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (HSMul.hSMul.{u2, u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) M M (instHSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) M (MulAction.toSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) M (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) _inst_2)) _inst_5)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M _inst_4) r x)
+  forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (HSMul.hSMul.{u2, u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) M M (instHSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) M (MulAction.toSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) M (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) _inst_2)) _inst_5)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M _inst_4) r x)
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_smul IsScalarTower.algebraMap_smulₓ'. -/
 theorem algebraMap_smul (r : R) (x : M) : algebraMap R A r • x = r • x := by
   rw [Algebra.algebraMap_eq_smul_one, smul_assoc, one_smul]
@@ -110,7 +110,7 @@ variable {R S A}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3], (forall (x : R), Eq.{succ u3} A (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => S -> A) (RingHom.hasCoeToFun.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))) -> (IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3], (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))) -> (IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8))
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3], (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))) -> (IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8))
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.of_algebra_map_eq IsScalarTower.of_algebraMap_eqₓ'. -/
 theorem of_algebraMap_eq [Algebra R A]
     (h : ∀ x, algebraMap R A x = algebraMap S A (algebraMap R S x)) : IsScalarTower R S A :=
@@ -142,7 +142,7 @@ theorem algebraMap_eq : algebraMap R A = (algebraMap S A).comp (algebraMap R S)
 lean 3 declaration is
   forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] (x : R), Eq.{succ u3} A (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => S -> A) (RingHom.hasCoeToFun.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))
 but is expected to have type
-  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))
+  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u3} S A (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u2, u3} S A _inst_2 _inst_3 _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) x))
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_apply IsScalarTower.algebraMap_applyₓ'. -/
 theorem algebraMap_apply (x : R) : algebraMap R A x = algebraMap S A (algebraMap R S x) := by
   rw [algebra_map_eq R S A, RingHom.comp_apply]
@@ -373,7 +373,7 @@ variable [Module R M] [Module A M] [IsScalarTower R A M]
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
 Case conversion may be inaccurate. Consider using '#align submodule.restrict_scalars_span Submodule.restrictScalars_spanₓ'. -/
 /-- If `A` is an `R`-algebra such that the induced morphism `R →+* A` is surjective, then the
 `R`-module generated by a set `X` equals the `A`-module generated by `X`. -/
@@ -390,7 +390,7 @@ theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X :
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.setLike.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.setLike.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.instSetLikeSubmodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.instSetLikeSubmodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_span_eq_span_of_surjective Submodule.coe_span_eq_span_of_surjectiveₓ'. -/
 theorem coe_span_eq_span_of_surjective (h : Function.Surjective (algebraMap R A)) (s : Set M) :
     (Submodule.span A s : Set M) = Submodule.span R s :=
@@ -504,7 +504,7 @@ variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
 Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image Submodule.span_algebraMap_imageₓ'. -/
 /-- A variant of `submodule.span_image` for `algebra_map`. -/
 theorem span_algebraMap_image (a : Set R) :
@@ -516,7 +516,7 @@ theorem span_algebraMap_image (a : Set R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Module.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u1, u2, u2} R S S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u2, u3} S T (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13))))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)))))] (a : Set.{u2} S), Eq.{succ u3} (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u3} S T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.restrictScalars.{u1, u2, u2, u3} R S S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u3, u1, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u1, u3, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toSMul.{u3, u1} R T (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R T (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R T (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (Module.toMulActionWithZero.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u1, u3, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toSMul.{u3, u1} R T (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R T (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R T (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (Module.toMulActionWithZero.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
 Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_towerₓ'. -/
 theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring T] [Module R S]
     [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
@@ -529,7 +529,7 @@ theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u2, u3} S T (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_12))))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)))))] (x : S) (a : Set.{u2} S), (Membership.Mem.{u2, u2} S (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.setLike.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.Mem.{u3, u3} T (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11)) T (Submodule.setLike.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u3} S T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (fun (_x : RingHom.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) => S -> T) (RingHom.hasCoeToFun.{u2, u3} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u3} T _inst_9)) (algebraMap.{u2, u3} S T _inst_8 _inst_9 _inst_12)) a)))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u3, u2, u1} R S T (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_12) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_11)] (x : S) (a : Set.{u2} S), (Membership.mem.{u2, u2} S (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.instSetLikeSubmodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => T) x) (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) T (Submodule.instSetLikeSubmodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8)] [_inst_11 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_12 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_13 : IsScalarTower.{u3, u2, u1} R S T (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_12) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_11)] (x : S) (a : Set.{u2} S), (Membership.mem.{u2, u2} S (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10)) S (Submodule.instSetLikeSubmodule.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10))) x (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_8) _inst_10) a)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) x) (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11)) T (Submodule.instSetLikeSubmodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_11) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_imageₓ'. -/
 theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Anne Baanen
 
 ! This file was ported from Lean 3 source module algebra.algebra.tower
-! leanprover-community/mathlib commit 71150516f28d9826c7341f8815b31f7d8770c212
+! leanprover-community/mathlib commit 832f7b9162039c28b9361289c8681f155cae758f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.Span
 /-!
 # Towers of algebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove basic facts about towers of algebra.
 
 An algebra tower A/S/R is expressed by having instances of `algebra A S`,

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -39,6 +39,12 @@ variable [AddCommMonoid M] [Module R M] [Module A M] [IsScalarTower R A M]
 
 variable {A}
 
+/- warning: algebra.lsmul -> Algebra.lsmul is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 _inst_4 _inst_5)
+but is expected to have type
+  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)
+Case conversion may be inaccurate. Consider using '#align algebra.lsmul Algebra.lsmulₓ'. -/
 /-- The `R`-algebra morphism `A → End (M)` corresponding to the representation of the algebra `A`
 on the `R`-module `M`.
 
@@ -54,6 +60,12 @@ def lsmul : A →ₐ[R] Module.End R M
   commutes' r := LinearMap.ext <| algebraMap_smul A r
 #align algebra.lsmul Algebra.lsmul
 
+/- warning: algebra.lsmul_coe -> Algebra.lsmul_coe is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {A : Type.{u2}} (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A 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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) ((fun (x._@.Mathlib.Algebra.Algebra.Tower._hyg.251 : A) (x._@.Mathlib.Algebra.Algebra.Tower._hyg.253 : M) => HSMul.hSMul.{u2, u3, u3} A M M (instHSMul.{u2, u3} A M (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6))))) x._@.Mathlib.Algebra.Algebra.Tower._hyg.251 x._@.Mathlib.Algebra.Algebra.Tower._hyg.253) a)
+Case conversion may be inaccurate. Consider using '#align algebra.lsmul_coe Algebra.lsmul_coeₓ'. -/
 @[simp]
 theorem lsmul_coe (a : A) : (lsmul R M a : M → M) = (· • ·) a :=
   rfl
@@ -71,6 +83,12 @@ variable [SMul R M] [MulAction A M] [IsScalarTower R A M]
 
 variable {R} (A) {M}
 
+/- warning: is_scalar_tower.algebra_map_smul -> IsScalarTower.algebraMap_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (MulAction.toHasSmul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (SMul.smul.{u2, u3} A M (MulAction.toHasSmul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (SMul.smul.{u1, u3} R M _inst_4 r x)
+but is expected to have type
+  forall {R : Type.{u1}} (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : SMul.{u1, u3} R M] [_inst_5 : MulAction.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))] [_inst_6 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u2, u3} A M (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) _inst_5) _inst_4] (r : R) (x : M), Eq.{succ u3} M (HSMul.hSMul.{u2, u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) M M (instHSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) M (MulAction.toSMul.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) M (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) _inst_2)) _inst_5)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) x) (HSMul.hSMul.{u1, u3, u3} R M M (instHSMul.{u1, u3} R M _inst_4) r x)
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_smul IsScalarTower.algebraMap_smulₓ'. -/
 theorem algebraMap_smul (r : R) (x : M) : algebraMap R A r • x = r • x := by
   rw [Algebra.algebraMap_eq_smul_one, smul_assoc, one_smul]
 #align is_scalar_tower.algebra_map_smul IsScalarTower.algebraMap_smul
@@ -85,16 +103,24 @@ variable [Algebra R S] [Algebra S A] [Algebra S B]
 
 variable {R S A}
 
+/- warning: is_scalar_tower.of_algebra_map_eq -> IsScalarTower.of_algebraMap_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_scalar_tower.of_algebra_map_eq IsScalarTower.of_algebraMap_eqₓ'. -/
 theorem of_algebraMap_eq [Algebra R A]
     (h : ∀ x, algebraMap R A x = algebraMap S A (algebraMap R S x)) : IsScalarTower R S A :=
   ⟨fun x y z => by simp_rw [Algebra.smul_def, RingHom.map_mul, mul_assoc, h]⟩
 #align is_scalar_tower.of_algebra_map_eq IsScalarTower.of_algebraMap_eq
 
+#print IsScalarTower.of_algebraMap_eq' /-
 /-- See note [partially-applied ext lemmas]. -/
 theorem of_algebraMap_eq' [Algebra R A]
     (h : algebraMap R A = (algebraMap S A).comp (algebraMap R S)) : IsScalarTower R S A :=
   of_algebraMap_eq <| RingHom.ext_iff.1 h
 #align is_scalar_tower.of_algebra_map_eq' IsScalarTower.of_algebraMap_eq'
+-/
 
 variable (R S A)
 
@@ -102,15 +128,24 @@ variable [Algebra R A] [Algebra R B]
 
 variable [IsScalarTower R S A] [IsScalarTower R S B]
 
+#print IsScalarTower.algebraMap_eq /-
 theorem algebraMap_eq : algebraMap R A = (algebraMap S A).comp (algebraMap R S) :=
   RingHom.ext fun x => by
     simp_rw [RingHom.comp_apply, Algebra.algebraMap_eq_smul_one, smul_assoc, one_smul]
 #align is_scalar_tower.algebra_map_eq IsScalarTower.algebraMap_eq
+-/
 
+/- warning: is_scalar_tower.algebra_map_apply -> IsScalarTower.algebraMap_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_scalar_tower.algebra_map_apply IsScalarTower.algebraMap_applyₓ'. -/
 theorem algebraMap_apply (x : R) : algebraMap R A x = algebraMap S A (algebraMap R S x) := by
   rw [algebra_map_eq R S A, RingHom.comp_apply]
 #align is_scalar_tower.algebra_map_apply IsScalarTower.algebraMap_apply
 
+#print IsScalarTower.Algebra.ext /-
 @[ext]
 theorem Algebra.ext {S : Type u} {A : Type v} [CommSemiring S] [Semiring A] (h1 h2 : Algebra S A)
     (h :
@@ -122,49 +157,78 @@ theorem Algebra.ext {S : Type u} {A : Type v} [CommSemiring S] [Semiring A] (h1
   Algebra.algebra_ext _ _ fun r => by
     simpa only [@Algebra.smul_def _ _ _ _ h1, @Algebra.smul_def _ _ _ _ h2, mul_one] using h r 1
 #align is_scalar_tower.algebra.ext IsScalarTower.Algebra.ext
+-/
 
+#print IsScalarTower.toAlgHom /-
 /-- In a tower, the canonical map from the middle element to the top element is an
 algebra homomorphism over the bottom element. -/
 def toAlgHom : S →ₐ[R] A :=
   { algebraMap S A with commutes' := fun _ => (algebraMap_apply _ _ _ _).symm }
 #align is_scalar_tower.to_alg_hom IsScalarTower.toAlgHom
+-/
 
+#print IsScalarTower.toAlgHom_apply /-
 theorem toAlgHom_apply (y : S) : toAlgHom R S A y = algebraMap S A y :=
   rfl
 #align is_scalar_tower.to_alg_hom_apply IsScalarTower.toAlgHom_apply
+-/
 
+/- warning: is_scalar_tower.coe_to_alg_hom -> IsScalarTower.coe_toAlgHom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_scalar_tower.coe_to_alg_hom IsScalarTower.coe_toAlgHomₓ'. -/
 @[simp]
 theorem coe_toAlgHom : ↑(toAlgHom R S A) = algebraMap S A :=
   RingHom.ext fun _ => rfl
 #align is_scalar_tower.coe_to_alg_hom IsScalarTower.coe_toAlgHom
 
+#print IsScalarTower.coe_to_alg_hom' /-
 @[simp]
 theorem coe_to_alg_hom' : (toAlgHom R S A : S → A) = algebraMap S A :=
   rfl
 #align is_scalar_tower.coe_to_alg_hom' IsScalarTower.coe_to_alg_hom'
+-/
 
 variable {R S A B}
 
+#print IsScalarTower.AlgHom.map_algebraMap /-
 @[simp]
-theorem AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) : f (algebraMap R A r) = algebraMap R B r :=
-  by rw [algebra_map_apply R S A r, f.commutes, ← algebra_map_apply R S B]
-#align alg_hom.map_algebra_map AlgHom.map_algebraMap
+theorem IsScalarTower.AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) :
+    f (algebraMap R A r) = algebraMap R B r := by
+  rw [algebra_map_apply R S A r, f.commutes, ← algebra_map_apply R S B]
+#align alg_hom.map_algebra_map IsScalarTower.AlgHom.map_algebraMap
+-/
 
 variable (R)
 
+/- warning: alg_hom.comp_algebra_map_of_tower -> IsScalarTower.AlgHom.comp_algebraMap_of_tower is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R 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(CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u1) (succ u4)} (RingHom.{u1, u4} R B (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (RingHom.comp.{u1, u3, u4} R A B (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (RingHom.hasCoeT.{max u3 u4, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) (AlgHomClass.toRingHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgHom.algHomClass.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7))))) f) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (algebraMap.{u1, u4} R B _inst_1 _inst_4 _inst_9)
+but is expected to have type
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u1) (succ u4)} (RingHom.{u1, u4} R B (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (RingHom.comp.{u1, u3, u4} R A B (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) (RingHomClass.toRingHom.{max u4 u3, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) (AlgHomClass.toRingHomClass.{max u4 u3, u2, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgHom.algHomClass.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)) f) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (algebraMap.{u1, u4} R B _inst_1 _inst_4 _inst_9)
+Case conversion may be inaccurate. Consider using '#align alg_hom.comp_algebra_map_of_tower IsScalarTower.AlgHom.comp_algebraMap_of_towerₓ'. -/
 @[simp]
-theorem AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
+theorem IsScalarTower.AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
     (f : A →+* B).comp (algebraMap R A) = algebraMap R B :=
   RingHom.ext f.map_algebraMap
-#align alg_hom.comp_algebra_map_of_tower AlgHom.comp_algebraMap_of_tower
+#align alg_hom.comp_algebra_map_of_tower IsScalarTower.AlgHom.comp_algebraMap_of_tower
 
 variable (R) {S A B}
 
+/- warning: is_scalar_tower.subsemiring -> IsScalarTower.subsemiring is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Semiring.{u2} A] [_inst_6 : Algebra.{u1, u2} S A _inst_2 _inst_3] (U : Subsemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))), IsScalarTower.{u1, u1, u2} (coeSort.{succ u1, succ (succ u1)} (Subsemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subsemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S (Subsemiring.setLike.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) U) S A (Subsemiring.hasSmul.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Mul.toSMul.{u1} S (Distrib.toHasMul.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) U) (SMulZeroClass.toHasSmul.{u1, u2} S A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} S A (MulZeroClass.toHasZero.{u1} S (MulZeroOneClass.toMulZeroClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} S A (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_6))))) (Subsemiring.hasSmul.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SMulZeroClass.toHasSmul.{u1, u2} S A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} S A (MulZeroClass.toHasZero.{u1} S (MulZeroOneClass.toMulZeroClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} S A (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_6))))) U)
+but is expected to have type
+  forall {S : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Semiring.{u2} A] [_inst_6 : Algebra.{u1, u2} S A _inst_2 _inst_3] (U : Subsemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))), IsScalarTower.{u1, u1, u2} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subsemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (SetLike.instMembership.{u1, u1} (Subsemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S (Subsemiring.instSetLikeSubsemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) x U)) S A (Subsemiring.smul.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Algebra.toSMul.{u1, u1} S S _inst_2 (CommSemiring.toSemiring.{u1} S _inst_2) (Algebra.id.{u1} S _inst_2)) U) (Algebra.toSMul.{u1, u2} S A _inst_2 _inst_3 _inst_6) (Subsemiring.smul.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Algebra.toSMul.{u1, u2} S A _inst_2 _inst_3 _inst_6) U)
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower.subsemiring IsScalarTower.subsemiringₓ'. -/
 -- conflicts with is_scalar_tower.subalgebra
 instance (priority := 999) subsemiring (U : Subsemiring S) : IsScalarTower U S A :=
   of_algebraMap_eq fun x => rfl
 #align is_scalar_tower.subsemiring IsScalarTower.subsemiring
 
+#print IsScalarTower.of_ring_hom /-
 @[nolint instance_priority]
 instance of_ring_hom {R A B : Type _} [CommSemiring R] [CommSemiring A] [CommSemiring B]
     [Algebra R A] [Algebra R B] (f : A →ₐ[R] B) :
@@ -172,6 +236,7 @@ instance of_ring_hom {R A B : Type _} [CommSemiring R] [CommSemiring A] [CommSem
   letI := (f : A →+* B).toAlgebra
   of_algebra_map_eq fun x => (f.commutes x).symm
 #align is_scalar_tower.of_ring_hom IsScalarTower.of_ring_hom
+-/
 
 end Semiring
 
@@ -193,6 +258,7 @@ open IsScalarTower
 
 namespace AlgHom
 
+#print AlgHom.restrictScalars /-
 /-- R ⟶ S induces S-Alg ⥤ R-Alg -/
 def restrictScalars (f : A →ₐ[S] B) : A →ₐ[R] B :=
   { (f : A →+* B) with
@@ -201,30 +267,44 @@ def restrictScalars (f : A →ₐ[S] B) : A →ₐ[R] B :=
       rw [algebra_map_apply R S A, algebra_map_apply R S B]
       exact f.commutes (algebraMap R S r) }
 #align alg_hom.restrict_scalars AlgHom.restrictScalars
+-/
 
+#print AlgHom.restrictScalars_apply /-
 theorem restrictScalars_apply (f : A →ₐ[S] B) (x : A) : f.restrictScalars R x = f x :=
   rfl
 #align alg_hom.restrict_scalars_apply AlgHom.restrictScalars_apply
+-/
 
+/- warning: alg_hom.coe_restrict_scalars -> AlgHom.coe_restrictScalars is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u3) (succ u4)} (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) 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_inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgHom.algHomClass.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9))))) (AlgHom.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (RingHom.hasCoeT.{max u3 u4, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) (AlgHomClass.toRingHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgHom.algHomClass.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7))))) f)
+but is expected to have type
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u4) (succ u3)} (RingHom.{u3, u4} A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (RingHomClass.toRingHom.{max u4 u3, u3, u4} (AlgHom.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) (AlgHomClass.toRingHomClass.{max u4 u3, u1, u3, u4} (AlgHom.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgHom.algHomClass.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)) (AlgHom.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (RingHomClass.toRingHom.{max u4 u3, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A B (Semiring.toNonAssocSemiring.{u3} A _inst_3) (Semiring.toNonAssocSemiring.{u4} B _inst_4) (AlgHomClass.toRingHomClass.{max u4 u3, u2, u3, u4} (AlgHom.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgHom.algHomClass.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)) f)
+Case conversion may be inaccurate. Consider using '#align alg_hom.coe_restrict_scalars AlgHom.coe_restrictScalarsₓ'. -/
 @[simp]
 theorem coe_restrictScalars (f : A →ₐ[S] B) : (f.restrictScalars R : A →+* B) = f :=
   rfl
 #align alg_hom.coe_restrict_scalars AlgHom.coe_restrictScalars
 
+#print AlgHom.coe_restrict_scalars' /-
 @[simp]
 theorem coe_restrict_scalars' (f : A →ₐ[S] B) : (restrictScalars R f : A → B) = f :=
   rfl
 #align alg_hom.coe_restrict_scalars' AlgHom.coe_restrict_scalars'
+-/
 
+#print AlgHom.restrictScalars_injective /-
 theorem restrictScalars_injective :
     Function.Injective (restrictScalars R : (A →ₐ[S] B) → A →ₐ[R] B) := fun f g h =>
   AlgHom.ext (AlgHom.congr_fun h : _)
 #align alg_hom.restrict_scalars_injective AlgHom.restrictScalars_injective
+-/
 
 end AlgHom
 
 namespace AlgEquiv
 
+#print AlgEquiv.restrictScalars /-
 /-- R ⟶ S induces S-Alg ⥤ R-Alg -/
 def restrictScalars (f : A ≃ₐ[S] B) : A ≃ₐ[R] B :=
   { (f : A ≃+* B) with
@@ -233,25 +313,46 @@ def restrictScalars (f : A ≃ₐ[S] B) : A ≃ₐ[R] B :=
       rw [algebra_map_apply R S A, algebra_map_apply R S B]
       exact f.commutes (algebraMap R S r) }
 #align alg_equiv.restrict_scalars AlgEquiv.restrictScalars
+-/
 
+/- warning: alg_equiv.restrict_scalars_apply -> AlgEquiv.restrictScalars_apply is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S 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(MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (x : A), Eq.{succ u4} B (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (fun (_x : AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) => A -> B) (AlgEquiv.hasCoeToFun.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) => A -> B) (AlgEquiv.hasCoeToFun.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) f x)
+but is expected to have type
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (x : A), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))) (SMulZeroClass.toSMul.{u1, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u4} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u1, u3, u4, max u4 u3} R A B (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9) (AlgHomClass.linearMapClass.{u1, u3, u4, max u4 u3} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u2, u4} S B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} S B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} S B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6)) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, u4, max u4 u3} S A B (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7) (AlgHomClass.linearMapClass.{u2, u3, u4, max u4 u3} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)))))) f x)
+Case conversion may be inaccurate. Consider using '#align alg_equiv.restrict_scalars_apply AlgEquiv.restrictScalars_applyₓ'. -/
 theorem restrictScalars_apply (f : A ≃ₐ[S] B) (x : A) : f.restrictScalars R x = f x :=
   rfl
 #align alg_equiv.restrict_scalars_apply AlgEquiv.restrictScalars_apply
 
+/- warning: alg_equiv.coe_restrict_scalars -> AlgEquiv.coe_restrictScalars is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S 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(MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u3) (succ u4)} (RingEquiv.{u3, u4} A B (Distrib.toHasMul.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasMul.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Distrib.toHasAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (RingEquiv.{u3, u4} A B (Distrib.toHasMul.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasMul.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Distrib.toHasAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (RingEquiv.{u3, u4} A B (Distrib.toHasMul.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toHasMul.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B 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(AlgEquiv.algEquivClass.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7))))) f)
+but is expected to have type
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u4) (succ u3)} (RingEquiv.{u3, u4} A B (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Distrib.toAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Distrib.toAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (RingEquivClass.toRingEquiv.{max u4 u3, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A B (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Distrib.toAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Distrib.toAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (AlgEquivClass.toRingEquivClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (RingEquivClass.toRingEquiv.{max u4 u3, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A B (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Distrib.toAdd.{u3} A (NonUnitalNonAssocSemiring.toDistrib.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Distrib.toAdd.{u4} B (NonUnitalNonAssocSemiring.toDistrib.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (AlgEquivClass.toRingEquivClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)) f)
+Case conversion may be inaccurate. Consider using '#align alg_equiv.coe_restrict_scalars AlgEquiv.coe_restrictScalarsₓ'. -/
 @[simp]
 theorem coe_restrictScalars (f : A ≃ₐ[S] B) : (f.restrictScalars R : A ≃+* B) = f :=
   rfl
 #align alg_equiv.coe_restrict_scalars AlgEquiv.coe_restrictScalars
 
+/- warning: alg_equiv.coe_restrict_scalars' -> AlgEquiv.coe_restrict_scalars' is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u4} S B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S B (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S B (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R B (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)))))] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u3) (succ u4)} ((fun (_x : AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) => A -> B) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (fun (_x : AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) => A -> B) (AlgEquiv.hasCoeToFun.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) => A -> B) (AlgEquiv.hasCoeToFun.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) f)
+but is expected to have type
+  forall (R : Type.{u1}) {S : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_7 : Algebra.{u2, u4} S B _inst_2 _inst_4] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_9 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} R S B (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u4} S B _inst_2 _inst_4 _inst_7) (Algebra.toSMul.{u1, u4} R B _inst_1 _inst_4 _inst_9)] (f : AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7), Eq.{max (succ u4) (succ u3)} (forall (a : A), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8))))) (SMulZeroClass.toSMul.{u1, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u4} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)) (Module.toDistribMulAction.{u1, u4} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u1, u3, u4, max u4 u3} R A B (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_9) (AlgHomClass.linearMapClass.{u1, u3, u4, max u4 u3} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u3, u1, u3, u4} (AlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9) R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u4} R A B _inst_1 _inst_3 _inst_4 _inst_8 _inst_9)))))) (AlgEquiv.restrictScalars.{u1, u2, u3, u4} R S A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 f)) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u2, u4} S B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} S B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} S B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6)) (Module.toDistribMulAction.{u2, u4} S B (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, u4, max u4 u3} S A B (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toModule.{u2, u4} S B _inst_2 _inst_4 _inst_7) (AlgHomClass.linearMapClass.{u2, u3, u4, max u4 u3} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u3, u2, u3, u4} (AlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7) S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} S A B _inst_2 _inst_3 _inst_4 _inst_6 _inst_7)))))) f)
+Case conversion may be inaccurate. Consider using '#align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrict_scalars'ₓ'. -/
 @[simp]
 theorem coe_restrict_scalars' (f : A ≃ₐ[S] B) : (restrictScalars R f : A → B) = f :=
   rfl
 #align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrict_scalars'
 
+#print AlgEquiv.restrictScalars_injective /-
 theorem restrictScalars_injective :
     Function.Injective (restrictScalars R : (A ≃ₐ[S] B) → A ≃ₐ[R] B) := fun f g h =>
   AlgEquiv.ext (AlgEquiv.congr_fun h : _)
 #align alg_equiv.restrict_scalars_injective AlgEquiv.restrictScalars_injective
+-/
 
 end AlgEquiv
 
@@ -265,6 +366,12 @@ variable [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M]
 
 variable [Module R M] [Module A M] [IsScalarTower R A M]
 
+/- warning: submodule.restrict_scalars_span -> Submodule.restrictScalars_span is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (X : Set.{u3} M), Eq.{succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.restrictScalars.{u1, u2, u3} R A M _inst_2 _inst_4 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 _inst_6 (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 X)) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 X))
+Case conversion may be inaccurate. Consider using '#align submodule.restrict_scalars_span Submodule.restrictScalars_spanₓ'. -/
 /-- If `A` is an `R`-algebra such that the induced morphism `R →+* A` is surjective, then the
 `R`-module generated by a set `X` equals the `A`-module generated by `X`. -/
 theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X : Set M) :
@@ -276,6 +383,12 @@ theorem restrictScalars_span (hsur : Function.Surjective (algebraMap R A)) (X :
   simpa [algebraMap_smul] using smul_mem _ r hm
 #align submodule.restrict_scalars_span Submodule.restrictScalars_span
 
+/- warning: submodule.coe_span_eq_span_of_surjective -> Submodule.coe_span_eq_span_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M 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_inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.setLike.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.setLike.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) {M : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))], (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (forall (s : Set.{u3} M), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) M (Submodule.instSetLikeSubmodule.{u2, u3} A M _inst_2 _inst_4 _inst_6) (Submodule.span.{u2, u3} A M _inst_2 _inst_4 _inst_6 s)) (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (Submodule.span.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5 s)))
+Case conversion may be inaccurate. Consider using '#align submodule.coe_span_eq_span_of_surjective Submodule.coe_span_eq_span_of_surjectiveₓ'. -/
 theorem coe_span_eq_span_of_surjective (h : Function.Surjective (algebraMap R A)) (s : Set M) :
     (Submodule.span A s : Set M) = Submodule.span R s :=
   congr_arg coe (Submodule.restrictScalars_span R A h s)
@@ -297,6 +410,12 @@ variable [Module R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
 open IsScalarTower
 
+/- warning: submodule.smul_mem_span_smul_of_mem -> Submodule.smul_mem_span_smul_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] {s : Set.{u2} S} {t : Set.{u3} A} {k : S}, (Membership.Mem.{u2, u2} S (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) S (Submodule.setLike.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)) k (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s)) -> (forall {x : A}, (Membership.Mem.{u3, u3} A (Set.{u3} A) (Set.hasMem.{u3} A) x t) -> (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (SMul.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] {s : Set.{u2} S} {t : Set.{u3} A} {k : S}, (Membership.mem.{u2, u2} S (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) S (Submodule.instSetLikeSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)) k (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s)) -> (forall {x : A}, (Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x t) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
+Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul_of_mem Submodule.smul_mem_span_smul_of_memₓ'. -/
 theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ span R s) {x : A}
     (hx : x ∈ t) : k • x ∈ span R (s • t) :=
   span_induction hks (fun c hc => subset_span <| Set.mem_smul.2 ⟨c, x, hc, hx, rfl⟩)
@@ -313,6 +432,12 @@ theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ s
 
 variable [SMulCommClass R S A]
 
+/- warning: submodule.smul_mem_span_smul -> Submodule.smul_mem_span_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.hasTop.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 t)) -> (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (SMul.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 t)) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
+Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul Submodule.smul_mem_span_smulₓ'. -/
 theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R t) : k • x ∈ span R (s • t) :=
   span_induction hx (fun x hx => smul_mem_span_smul_of_mem (hs.symm ▸ mem_top) hx)
@@ -325,6 +450,12 @@ theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S}
     fun c x hx => smul_comm c k x ▸ smul_mem _ _ hx
 #align submodule.smul_mem_span_smul Submodule.smul_mem_span_smul
 
+/- warning: submodule.smul_mem_span_smul' -> Submodule.smul_mem_span_smul' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.hasTop.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))) -> (Membership.Mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.setLike.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (SMul.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall {t : Set.{u3} A} {k : S} {x : A}, (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) x (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))) -> (Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) A (Submodule.instSetLikeSubmodule.{u1, u3} R A _inst_1 _inst_3 _inst_6)) (HSMul.hSMul.{u2, u3, u3} S A A (instHSMul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) k x) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t))))
+Case conversion may be inaccurate. Consider using '#align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'ₓ'. -/
 theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
     (hx : x ∈ span R (s • t)) : k • x ∈ span R (s • t) :=
   span_induction hx
@@ -341,6 +472,12 @@ theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S
     fun c x hx => smul_comm c k x ▸ smul_mem _ _ hx
 #align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'
 
+/- warning: submodule.span_smul_of_span_eq_top -> Submodule.span_smul_of_span_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.hasTop.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall (t : Set.{u3} A), Eq.{succ u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (SMul.smul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))) s t)) (Submodule.restrictScalars.{u1, u2, u3} R S A _inst_2 _inst_3 _inst_1 _inst_6 _inst_5 (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) _inst_7 (Submodule.span.{u2, u3} S A _inst_2 _inst_3 _inst_5 t)))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6))))] [_inst_8 : SMulCommClass.{u1, u2, u3} R S A (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A _inst_1 _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5))))] {s : Set.{u2} S}, (Eq.{succ u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.span.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4 s) (Top.top.{u2} (Submodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4))) -> (forall (t : Set.{u3} A), Eq.{succ u3} (Submodule.{u1, u3} R A _inst_1 _inst_3 _inst_6) (Submodule.span.{u1, u3} R A _inst_1 _inst_3 _inst_6 (HSMul.hSMul.{u2, u3, u3} (Set.{u2} S) (Set.{u3} A) (Set.{u3} A) (instHSMul.{u2, u3} (Set.{u2} S) (Set.{u3} A) (Set.smul.{u2, u3} S A (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))))) s t)) (Submodule.restrictScalars.{u1, u2, u3} R S A _inst_2 _inst_3 _inst_1 _inst_6 _inst_5 (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) _inst_7 (Submodule.span.{u2, u3} S A _inst_2 _inst_3 _inst_5 t)))
+Case conversion may be inaccurate. Consider using '#align submodule.span_smul_of_span_eq_top Submodule.span_smul_of_span_eq_topₓ'. -/
 theorem span_smul_of_span_eq_top {s : Set S} (hs : span R s = ⊤) (t : Set A) :
     span R (s • t) = (span S t).restrictScalars R :=
   le_antisymm
@@ -360,12 +497,24 @@ variable [CommSemiring R] [Semiring S] [AddCommMonoid A]
 
 variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
+/- warning: submodule.span_algebra_map_image -> Submodule.span_algebraMap_image is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] (a : Set.{u1} R), Eq.{succ u2} (Submodule.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Set.image.{u1, u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_4)) a)) (Submodule.map.{u1, u1, u1, u2, max u1 u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u2} R R R S (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.linearMap.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
+Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image Submodule.span_algebraMap_imageₓ'. -/
 /-- A variant of `submodule.span_image` for `algebra_map`. -/
 theorem span_algebraMap_image (a : Set R) :
     Submodule.span R (algebraMap R S '' a) = (Submodule.span R a).map (Algebra.linearMap R S) :=
   (Submodule.span_image <| Algebra.linearMap R S).trans rfl
 #align submodule.span_algebra_map_image Submodule.span_algebraMap_image
 
+/- warning: submodule.span_algebra_map_image_of_tower -> Submodule.span_algebraMap_image_of_tower is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} {T : Type.{u3}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u3} T] [_inst_10 : Module.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u1, u2, u2} R S S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u1, u3} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u3} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S 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(AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.restrictScalars.{u1, u2, u2, u3} R S S T (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) _inst_10 (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u3, u1, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9)))))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_9))) (Algebra.toModule.{u1, u3} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u3} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u3} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} {T : Type.{u1}} [_inst_8 : CommSemiring.{u2} S] [_inst_9 : Semiring.{u1} T] [_inst_10 : Module.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))))] [_inst_11 : IsScalarTower.{u3, u2, u2} R S S (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u2} S S _inst_8 (CommSemiring.toSemiring.{u2} S _inst_8) (Algebra.id.{u2} S _inst_8)) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10))))] [_inst_12 : Algebra.{u3, u1} R T _inst_1 _inst_9] [_inst_13 : Algebra.{u2, u1} S T _inst_8 _inst_9] [_inst_14 : IsScalarTower.{u3, u2, u1} R S T (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Algebra.toSMul.{u2, u1} S T _inst_8 _inst_9 _inst_13) (Algebra.toSMul.{u3, u1} R T _inst_1 _inst_9 _inst_12)] (a : Set.{u2} S), Eq.{succ u1} (Submodule.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Set.image.{u2, u1} S T (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) a)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12)) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.restrictScalars.{u3, u2, u2, u1} R S S T (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) _inst_10 (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) (LinearMap.IsScalarTower.compatibleSMul.{u2, u1, u3, u2} S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) R S (CommSemiring.toSemiring.{u2} S _inst_8) (SMulZeroClass.toSMul.{u3, u2} R S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S _inst_8)) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R S (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R S (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))))) (Module.toMulActionWithZero.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) _inst_11 (SMulZeroClass.toSMul.{u3, u1} R T (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R T (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R T (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} T (AddCommMonoid.toAddMonoid.{u1} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (Module.toMulActionWithZero.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (Algebra.toModule.{u3, u1} R T _inst_1 _inst_9 _inst_12))))) (Algebra.toModule.{u2, u1} S T _inst_8 _inst_9 _inst_13) _inst_14) (Algebra.linearMap.{u2, u1} S T _inst_8 _inst_9 _inst_13)) (Submodule.span.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) _inst_10 a))
+Case conversion may be inaccurate. Consider using '#align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_towerₓ'. -/
 theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring T] [Module R S]
     [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
     Submodule.span R (algebraMap S T '' a) =
@@ -373,6 +522,12 @@ theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring
   (Submodule.span_image <| (Algebra.linearMap S T).restrictScalars R).trans rfl
 #align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_tower
 
+/- warning: submodule.map_mem_span_algebra_map_image -> Submodule.map_mem_span_algebraMap_image is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_9 _inst_11))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12) x) (Submodule.span.{u3, u1} R T (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_9)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9)) S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9) (RingHom.instRingHomClassRingHom.{u2, u1} S T (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_8)) (Semiring.toNonAssocSemiring.{u1} T _inst_9))))) (algebraMap.{u2, u1} S T _inst_8 _inst_9 _inst_12)) a)))
+Case conversion may be inaccurate. Consider using '#align submodule.map_mem_span_algebra_map_image Submodule.map_mem_span_algebraMap_imageₓ'. -/
 theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)
     (hx : x ∈ Submodule.span R a) : algebraMap S T x ∈ Submodule.span R (algebraMap S T '' a) :=
@@ -395,6 +550,12 @@ variable [CommSemiring R] [Semiring A] [Algebra R A]
 
 variable [AddCommGroup M] [Module A M] [Module R M] [IsScalarTower R A M]
 
+/- warning: algebra.lsmul_injective -> Algebra.lsmul_injective is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) -> (Function.Injective.{succ u3, succ u3} M M (coeFn.{succ u3, succ u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (fun (_x : AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) => A -> (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) ([anonymous].{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.End.algebra.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) (M : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_6 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} A M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u3} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_4))))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_5))))] {x : A}, (Ne.{succ u2} A x (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2))))) -> (Function.Injective.{succ u3, succ u3} M M (FunLike.coe.{succ u3, succ u3, succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) x) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _x) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toZero.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) (AlgHom.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)) (AlgHom.algHomClass.{u1, u2, u3} R A (Module.End.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_1 _inst_2 (Module.End.semiring.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6)))))) (Algebra.lsmul.{u1, u2, u3} R A M _inst_1 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) _inst_6 _inst_5 _inst_7) x)))
+Case conversion may be inaccurate. Consider using '#align algebra.lsmul_injective Algebra.lsmul_injectiveₓ'. -/
 theorem lsmul_injective [NoZeroSMulDivisors A M] {x : A} (hx : x ≠ 0) :
     Function.Injective (lsmul R M x) :=
   smul_right_injective _ hx

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

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

@@ -177,7 +177,7 @@ instance (priority := 999) subsemiring (U : Subsemiring S) : IsScalarTower U S A
   of_algebraMap_eq fun _x => rfl
 #align is_scalar_tower.subsemiring IsScalarTower.subsemiring
 
--- Porting note: @[nolint instance_priority]
+-- Porting note(#12096): removed @[nolint instance_priority], linter not ported yet
 instance (priority := 999) of_algHom {R A B : Type*} [CommSemiring R] [CommSemiring A]
     [CommSemiring B] [Algebra R A] [Algebra R B] (f : A →ₐ[R] B) :
     @IsScalarTower R A B _ f.toRingHom.toAlgebra.toSMul _ :=

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -33,7 +33,6 @@ namespace Algebra
 variable [CommSemiring R] [Semiring A] [Semiring B] [Algebra R A] [Algebra R B]
 variable [AddCommMonoid M] [Module R M] [Module A M] [Module B M]
 variable [IsScalarTower R A M] [IsScalarTower R B M] [SMulCommClass A B M]
-
 variable {A}
 
 
@@ -83,9 +82,7 @@ namespace IsScalarTower
 section Module
 
 variable [CommSemiring R] [Semiring A] [Algebra R A]
-
 variable [MulAction A M]
-
 variable {R} {M}
 
 theorem algebraMap_smul [SMul R M] [IsScalarTower R A M] (r : R) (x : M) :
@@ -107,9 +104,7 @@ end Module
 section Semiring
 
 variable [CommSemiring R] [CommSemiring S] [Semiring A] [Semiring B]
-
 variable [Algebra R S] [Algebra S A] [Algebra S B]
-
 variable {R S A}
 
 theorem of_algebraMap_eq [Algebra R A]
@@ -124,9 +119,7 @@ theorem of_algebraMap_eq' [Algebra R A]
 #align is_scalar_tower.of_algebra_map_eq' IsScalarTower.of_algebraMap_eq'
 
 variable (R S A)
-
 variable [Algebra R A] [Algebra R B]
-
 variable [IsScalarTower R S A] [IsScalarTower R S B]
 
 theorem algebraMap_eq : algebraMap R A = (algebraMap S A).comp (algebraMap R S) :=
@@ -199,13 +192,9 @@ end IsScalarTower
 section Homs
 
 variable [CommSemiring R] [CommSemiring S] [Semiring A] [Semiring B]
-
 variable [Algebra R S] [Algebra S A] [Algebra S B]
-
 variable [Algebra R A] [Algebra R B]
-
 variable [IsScalarTower R S A] [IsScalarTower R S B]
-
 variable {A S B}
 
 open IsScalarTower
@@ -271,9 +260,7 @@ end Homs
 namespace Submodule
 
 variable {M}
-
 variable [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M]
-
 variable [Module R M] [Module A M] [IsScalarTower R A M]
 
 /-- If `A` is an `R`-algebra such that the induced morphism `R →+* A` is surjective, then the
@@ -302,7 +289,6 @@ namespace Submodule
 section Module
 
 variable [Semiring R] [Semiring S] [AddCommMonoid A]
-
 variable [Module R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
 open IsScalarTower
@@ -345,7 +331,6 @@ end Module
 section Algebra
 
 variable [CommSemiring R] [Semiring S] [AddCommMonoid A]
-
 variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
 /-- A variant of `Submodule.span_image` for `algebraMap`. -/

• Prove isSemisimple_of_mem_adjoin: if two commuting endomorphisms of a finite-dimensional vector space over a perfect field are both semisimple, then every endomorphism in the algebra generated by them (in particular their product and sum) is semisimple.

• In the same file LinearAlgebra/Semisimple.lean, eq_zero_of_isNilpotent_isSemisimple and isSemisimple_of_squarefree_aeval_eq_zero are golfed, and IsSemisimple.minpoly_squarefree is proved

RingTheory/SimpleModule.lean:

• Define IsSemisimpleRing R to mean that R is a semisimple R-module. add properties of simple modules and a characterization (they are exactly the quotients of the ring by maximal left ideals).

• The annihilator of a semisimple module is a radical ideal.

• Any module over a semisimple ring is semisimple.

• A finite product of semisimple rings is semisimple.

• Any quotient of a semisimple ring is semisimple.

• Add Artin--Wedderburn as a TODO (proof_wanted).

• Order/Atoms.lean: add the instance from IsSimpleOrder to ComplementedLattice, so that IsSimpleModule → IsSemisimpleModule is automatically inferred.

Prerequisites for showing a product of semisimple rings is semisimple:

• Algebra/Module/Submodule/Map.lean: generalize orderIsoMapComap so that it only requires RingHomSurjective rather than RingHomInvPair

• Algebra/Ring/CompTypeclasses.lean, Mathlib/Algebra/Ring/Pi.lean, Algebra/Ring/Prod.lean: add RingHomSurjective instances

RingTheory/Artinian.lean:

• quotNilradicalEquivPi: the quotient of a commutative Artinian ring R by its nilradical is isomorphic to the (finite) product of its quotients by maximal ideals (therefore a product of fields). equivPi: if the ring is moreover reduced, then the ring itself is a product of fields. Deduce that R is a semisimple ring and both R and R[X] are decomposition monoids. Requires RingEquiv.quotientBot in RingTheory/Ideal/QuotientOperations.lean.

• Data/Polynomial/Eval.lean: the polynomial ring over a finite product of rings is isomorphic to the product of polynomial rings over individual rings. (Used to show R[X] is a decomposition monoid.)

Other necessary results:

• FieldTheory/Minpoly/Field.lean: the minimal polynomial of an element in a reduced algebra over a field is radical.

• RingTheory/PowerBasis.lean: generalize PowerBasis.finiteDimensional and rename it to .finite.

Annihilator stuff, some of which do not end up being used:

• RingTheory/Ideal/Operations.lean: define Module.annihilator and redefine Submodule.annihilator in terms of it; add lemmas, including one that says an arbitrary intersection of radical ideals is radical. The new lemma Ideal.isRadical_iff_pow_one_lt depends on pow_imp_self_of_one_lt in Mathlib/Data/Nat/Interval.lean, which is also used to golf the proof of isRadical_iff_pow_one_lt.

• Algebra/Module/Torsion.lean: add a lemma and an instance (unused)

• Data/Polynomial/Module/Basic.lean: add a def (unused) and a lemma

• LinearAlgebra/AnnihilatingPolynomial.lean: add lemma span_minpoly_eq_annihilator

Some results about idempotent linear maps (projections) and idempotent elements, used to show that any (left) ideal in a semisimple ring is spanned by an idempotent element (unused):

• LinearAlgebra/Projection.lean: add def isIdempotentElemEquiv

• LinearAlgebra/Span.lean: add two lemmas

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -84,14 +84,24 @@ section Module
 
 variable [CommSemiring R] [Semiring A] [Algebra R A]
 
-variable [SMul R M] [MulAction A M] [IsScalarTower R A M]
+variable [MulAction A M]
 
 variable {R} {M}
 
-theorem algebraMap_smul (r : R) (x : M) : algebraMap R A r • x = r • x := by
+theorem algebraMap_smul [SMul R M] [IsScalarTower R A M] (r : R) (x : M) :
+    algebraMap R A r • x = r • x := by
   rw [Algebra.algebraMap_eq_smul_one, smul_assoc, one_smul]
 #align is_scalar_tower.algebra_map_smul IsScalarTower.algebraMap_smul
 
+variable {A} in
+theorem of_algebraMap_smul [SMul R M] (h : ∀ (r : R) (x : M), algebraMap R A r • x = r • x) :
+    IsScalarTower R A M where
+  smul_assoc r a x := by rw [Algebra.smul_def, mul_smul, h]
+
+variable (R M) in
+theorem of_compHom : letI := MulAction.compHom M (algebraMap R A : R →* A); IsScalarTower R A M :=
+  letI := MulAction.compHom M (algebraMap R A : R →* A); of_algebraMap_smul fun _ _ ↦ rfl
+
 end Module
 
 section Semiring

Add various LinearMap.CompatibleSMul instances that ultimately lead to generalization of Basis.smul to allow a noncommutative base ring. The key observations that allows the generalization are IsScalarTower.smulHomClass and isScalarTower_of_injective.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -345,7 +345,7 @@ theorem span_algebraMap_image (a : Set R) :
 #align submodule.span_algebra_map_image Submodule.span_algebraMap_image
 
 theorem span_algebraMap_image_of_tower {S T : Type*} [CommSemiring S] [Semiring T] [Module R S]
-    [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
+    [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
     Submodule.span R (algebraMap S T '' a) =
       (Submodule.span R a).map ((Algebra.linearMap S T).restrictScalars R) :=
   (Submodule.span_image <| (Algebra.linearMap S T).restrictScalars R).trans rfl

Add span_eq_closure and closure_induction which say that Submodule.span R s is generated by R • s as an AddSubmonoid. I feel that the existing span_induction should be replaced by closure_induction as the latter is stronger, and allow us to remove the commutativity condition in span_smul_of_span_eq_top in Algebra/Tower and generalize Module.Finite.trans to allow a non-commutative base ring.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -305,39 +305,31 @@ theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ s
     fun b c hc => by rw [IsScalarTower.smul_assoc]; exact smul_mem _ _ hc
 #align submodule.smul_mem_span_smul_of_mem Submodule.smul_mem_span_smul_of_mem
 
-variable [SMulCommClass R S A]
-
-theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
-    (hx : x ∈ span R t) : k • x ∈ span R (s • t) :=
-  span_induction hx (fun x hx => smul_mem_span_smul_of_mem (hs.symm ▸ mem_top) hx)
-    (by rw [smul_zero]; exact zero_mem _)
-    (fun x y ihx ihy => by rw [smul_add]; exact add_mem ihx ihy)
-    fun c x hx => smul_comm c k x ▸ smul_mem _ _ hx
-#align submodule.smul_mem_span_smul Submodule.smul_mem_span_smul
-
-theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
-    (hx : x ∈ span R (s • t)) : k • x ∈ span R (s • t) :=
-  span_induction hx
-    (fun x hx => by
-      let ⟨p, _hp, q, hq, hpq⟩ := Set.mem_smul.1 hx
-      rw [← hpq, smul_smul]
-      exact smul_mem_span_smul_of_mem (hs.symm ▸ mem_top) hq)
-    (by rw [smul_zero]; exact zero_mem _)
-    (fun x y ihx ihy => by rw [smul_add]; exact add_mem ihx ihy)
-    fun c x hx => smul_comm c k x ▸ smul_mem _ _ hx
-#align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'
-
 theorem span_smul_of_span_eq_top {s : Set S} (hs : span R s = ⊤) (t : Set A) :
     span R (s • t) = (span S t).restrictScalars R :=
   le_antisymm
-    (span_le.2 fun _x hx =>
-      let ⟨p, _q, _hps, hqt, hpqx⟩ := Set.mem_smul.1 hx
-      hpqx ▸ (span S t).smul_mem p (subset_span hqt))
-    fun _p hp =>
-    span_induction hp (fun x hx => one_smul S x ▸ smul_mem_span_smul hs (subset_span hx))
-      (zero_mem _) (fun _ _ => add_mem) fun _k _x hx => smul_mem_span_smul' hs hx
+    (span_le.2 fun _x ⟨p, _hps, _q, hqt, hpqx⟩ ↦ hpqx ▸ (span S t).smul_mem p (subset_span hqt))
+    fun p hp ↦ closure_induction hp (zero_mem _) (fun _ _ ↦ add_mem) fun s0 y hy ↦ by
+      refine span_induction (hs ▸ mem_top : s0 ∈ span R s)
+        (fun x hx ↦ subset_span ⟨x, hx, y, hy, rfl⟩) ?_ ?_ ?_
+      · rw [zero_smul]; apply zero_mem
+      · intro _ _; rw [add_smul]; apply add_mem
+      · intro r s0 hy; rw [IsScalarTower.smul_assoc]; exact smul_mem _ r hy
 #align submodule.span_smul_of_span_eq_top Submodule.span_smul_of_span_eq_top
 
+-- The following two lemmas were originally used to prove `span_smul_of_span_eq_top`
+-- but are now not needed.
+theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
+    (hx : x ∈ span R (s • t)) : k • x ∈ span R (s • t) := by
+  rw [span_smul_of_span_eq_top hs] at hx ⊢; exact (span S t).smul_mem k hx
+#align submodule.smul_mem_span_smul' Submodule.smul_mem_span_smul'
+
+theorem smul_mem_span_smul {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S} {x : A}
+    (hx : x ∈ span R t) : k • x ∈ span R (s • t) := by
+  rw [span_smul_of_span_eq_top hs]
+  exact (span S t).smul_mem k (span_le_restrictScalars R S t hx)
+#align submodule.smul_mem_span_smul Submodule.smul_mem_span_smul
+
 end Module
 
 section Algebra

It's about AlgHom not RingHom.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -175,12 +175,12 @@ instance (priority := 999) subsemiring (U : Subsemiring S) : IsScalarTower U S A
 #align is_scalar_tower.subsemiring IsScalarTower.subsemiring
 
 -- Porting note: @[nolint instance_priority]
-instance (priority := 999) of_ring_hom {R A B : Type*} [CommSemiring R] [CommSemiring A]
+instance (priority := 999) of_algHom {R A B : Type*} [CommSemiring R] [CommSemiring A]
     [CommSemiring B] [Algebra R A] [Algebra R B] (f : A →ₐ[R] B) :
     @IsScalarTower R A B _ f.toRingHom.toAlgebra.toSMul _ :=
   letI := (f : A →+* B).toAlgebra
   of_algebraMap_eq fun x => (f.commutes x).symm
-#align is_scalar_tower.of_ring_hom IsScalarTower.of_ring_hom
+#align is_scalar_tower.of_ring_hom IsScalarTower.of_algHom
 
 end Semiring
 

• Redefine Set.image2 to use ∃ a ∈ s, ∃ b ∈ t, f a b = c instead of ∃ a b, a ∈ s ∧ b ∈ t ∧ f a b = c.
• Redefine Set.seq as Set.image2. The new definition is equal to the old one but rw [Set.seq] gives a different result.
• Redefine Filter.map₂ to use ∃ u ∈ f, ∃ v ∈ g, image2 m u v ⊆ s instead of ∃ u v, u ∈ f ∧ v ∈ g ∧ ...
• Update lemmas like Set.mem_image2, Finset.mem_image₂, Set.mem_mul, Finset.mem_div etc

The two reasons to make the change are:

• ∃ a ∈ s, ∃ b ∈ t, _ is a simp-normal form, and
• it looks a bit nicer.

@@ -299,7 +299,7 @@ open IsScalarTower
 
 theorem smul_mem_span_smul_of_mem {s : Set S} {t : Set A} {k : S} (hks : k ∈ span R s) {x : A}
     (hx : x ∈ t) : k • x ∈ span R (s • t) :=
-  span_induction hks (fun c hc => subset_span <| Set.mem_smul.2 ⟨c, x, hc, hx, rfl⟩)
+  span_induction hks (fun c hc => subset_span <| Set.smul_mem_smul hc hx)
     (by rw [zero_smul]; exact zero_mem _)
     (fun c₁ c₂ ih₁ ih₂ => by rw [add_smul]; exact add_mem ih₁ ih₂)
     fun b c hc => by rw [IsScalarTower.smul_assoc]; exact smul_mem _ _ hc
@@ -319,7 +319,7 @@ theorem smul_mem_span_smul' {s : Set S} (hs : span R s = ⊤) {t : Set A} {k : S
     (hx : x ∈ span R (s • t)) : k • x ∈ span R (s • t) :=
   span_induction hx
     (fun x hx => by
-      let ⟨p, q, _hp, hq, hpq⟩ := Set.mem_smul.1 hx
+      let ⟨p, _hp, q, hq, hpq⟩ := Set.mem_smul.1 hx
       rw [← hpq, smul_smul]
       exact smul_mem_span_smul_of_mem (hs.symm ▸ mem_top) hq)
     (by rw [smul_zero]; exact zero_mem _)

I used the regex \(\(· (.) ·\) (.)\), replacing with ($2 $1 ·).

@@ -73,7 +73,7 @@ def lsmul : A →ₐ[R] Module.End B M where
 #align algebra.lsmul Algebra.lsmulₓ
 
 @[simp]
-theorem lsmul_coe (a : A) : (lsmul R B M a : M → M) = (· • ·) a := rfl
+theorem lsmul_coe (a : A) : (lsmul R B M a : M → M) = (a • ·) := rfl
 #align algebra.lsmul_coe Algebra.lsmul_coe
 
 end Algebra

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

@@ -157,8 +157,8 @@ variable {R S A B}
 
 @[simp]
 theorem _root_.AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) :
-    f (algebraMap R A r) = algebraMap R B r :=
-  by rw [algebraMap_apply R S A r, f.commutes, ← algebraMap_apply R S B]
+    f (algebraMap R A r) = algebraMap R B r := by
+  rw [algebraMap_apply R S A r, f.commutes, ← algebraMap_apply R S B]
 #align alg_hom.map_algebra_map AlgHom.map_algebraMap
 
 variable (R)

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

This has nice performance benefits.

@@ -175,7 +175,7 @@ instance (priority := 999) subsemiring (U : Subsemiring S) : IsScalarTower U S A
 #align is_scalar_tower.subsemiring IsScalarTower.subsemiring
 
 -- Porting note: @[nolint instance_priority]
-instance (priority := 999) of_ring_hom {R A B : Type _} [CommSemiring R] [CommSemiring A]
+instance (priority := 999) of_ring_hom {R A B : Type*} [CommSemiring R] [CommSemiring A]
     [CommSemiring B] [Algebra R A] [Algebra R B] (f : A →ₐ[R] B) :
     @IsScalarTower R A B _ f.toRingHom.toAlgebra.toSMul _ :=
   letI := (f : A →+* B).toAlgebra
@@ -352,14 +352,14 @@ theorem span_algebraMap_image (a : Set R) :
   (Submodule.span_image <| Algebra.linearMap R S).trans rfl
 #align submodule.span_algebra_map_image Submodule.span_algebraMap_image
 
-theorem span_algebraMap_image_of_tower {S T : Type _} [CommSemiring S] [Semiring T] [Module R S]
+theorem span_algebraMap_image_of_tower {S T : Type*} [CommSemiring S] [Semiring T] [Module R S]
     [IsScalarTower R S S] [Algebra R T] [Algebra S T] [IsScalarTower R S T] (a : Set S) :
     Submodule.span R (algebraMap S T '' a) =
       (Submodule.span R a).map ((Algebra.linearMap S T).restrictScalars R) :=
   (Submodule.span_image <| (Algebra.linearMap S T).restrictScalars R).trans rfl
 #align submodule.span_algebra_map_image_of_tower Submodule.span_algebraMap_image_of_tower
 
-theorem map_mem_span_algebraMap_image {S T : Type _} [CommSemiring S] [Semiring T] [Algebra R S]
+theorem map_mem_span_algebraMap_image {S T : Type*} [CommSemiring S] [Semiring T] [Algebra R S]
     [Algebra R T] [Algebra S T] [IsScalarTower R S T] (x : S) (a : Set S)
     (hx : x ∈ Submodule.span R a) : algebraMap S T x ∈ Submodule.span R (algebraMap S T '' a) := by
   rw [span_algebraMap_image_of_tower, mem_map]

This generalizes from Algebra.lsmul R M : A →ₐ[R] Module.End R M to Algebra.lsmul R S M : A →ₐ[R] Module.End S M.

This generalization was previously not possible because Module.End S M was not an R-algebra.

Notably this now allows things like Algebra.lsmul R A A : Aᵐᵒᵖ →ₐ[R] Module.End A A (right multiplication).

This doesn't bother attempting to generalize uses in downstream files, as most of them probably do not need the generality. Instead, we just replace Algebra.lsmul R with Algebra.lsmul R R.

@@ -30,28 +30,50 @@ variable (R : Type u) (S : Type v) (A : Type w) (B : Type u₁) (M : Type v₁)
 
 namespace Algebra
 
-variable [CommSemiring R] [Semiring A] [Algebra R A]
-
-variable [AddCommMonoid M] [Module R M] [Module A M] [IsScalarTower R A M]
+variable [CommSemiring R] [Semiring A] [Semiring B] [Algebra R A] [Algebra R B]
+variable [AddCommMonoid M] [Module R M] [Module A M] [Module B M]
+variable [IsScalarTower R A M] [IsScalarTower R B M] [SMulCommClass A B M]
 
 variable {A}
 
+
 /-- The `R`-algebra morphism `A → End (M)` corresponding to the representation of the algebra `A`
-on the `R`-module `M`.
+on the `B`-module `M`.
 
 This is a stronger version of `DistribMulAction.toLinearMap`, and could also have been
-called `Algebra.toModuleEnd`. -/
-def lsmul : A →ₐ[R] Module.End R M where
-  toFun := DistribMulAction.toLinearMap R M
+called `Algebra.toModuleEnd`.
+
+The typeclasses correspond to the situation where the types act on each other as
+```
+R ----→ B
+| ⟍     |
+|   ⟍   |
+↓     ↘ ↓
+A ----→ M
+```
+where the diagram commutes, the action by `R` commutes with everything, and the action by `A` and
+`B` on `M` commute.
+
+Typically this is most useful with `B = R` as `Algebra.lsmul R R A : A →ₐ[R] Module.End R M`.
+However this can be used to get the fact that left-multiplication by `A` is right `A`-linear, and
+vice versa, as
+```lean
+example : A →ₐ[R] Module.End Aᵐᵒᵖ A := Algebra.lsmul R Aᵐᵒᵖ A
+example : Aᵐᵒᵖ →ₐ[R] Module.End A A := Algebra.lsmul R A A
+```
+respectively; though `LinearMap.mulLeft` and `LinearMap.mulRight` can also be used here.
+-/
+def lsmul : A →ₐ[R] Module.End B M where
+  toFun := DistribMulAction.toLinearMap B M
   map_one' := LinearMap.ext fun _ => one_smul A _
   map_mul' a b := LinearMap.ext <| smul_assoc a b
   map_zero' := LinearMap.ext fun _ => zero_smul A _
   map_add' _a _b := LinearMap.ext fun _ => add_smul _ _ _
   commutes' r := LinearMap.ext <| algebraMap_smul A r
-#align algebra.lsmul Algebra.lsmul
+#align algebra.lsmul Algebra.lsmulₓ
 
 @[simp]
-theorem lsmul_coe (a : A) : (lsmul R M a : M → M) = (· • ·) a := rfl
+theorem lsmul_coe (a : A) : (lsmul R B M a : M → M) = (· • ·) a := rfl
 #align algebra.lsmul_coe Algebra.lsmul_coe
 
 end Algebra
@@ -354,13 +376,13 @@ section Ring
 
 namespace Algebra
 
-variable [CommSemiring R] [Semiring A] [Algebra R A]
-
-variable [AddCommGroup M] [Module A M] [Module R M] [IsScalarTower R A M]
+variable [CommSemiring R] [Semiring A] [Semiring B] [Algebra R A] [Algebra R B]
+variable [AddCommGroup M] [Module R M] [Module A M] [Module B M]
+variable [IsScalarTower R A M] [IsScalarTower R B M] [SMulCommClass A B M]
 
 theorem lsmul_injective [NoZeroSMulDivisors A M] {x : A} (hx : x ≠ 0) :
-    Function.Injective (lsmul R M x) :=
-  smul_right_injective _ hx
+    Function.Injective (lsmul R B M x) :=
+  smul_right_injective M hx
 #align algebra.lsmul_injective Algebra.lsmul_injective
 
 end Algebra

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Anne Baanen
-
-! This file was ported from Lean 3 source module algebra.algebra.tower
-! leanprover-community/mathlib commit 71150516f28d9826c7341f8815b31f7d8770c212
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Equiv
 import Mathlib.LinearAlgebra.Span
 
+#align_import algebra.algebra.tower from "leanprover-community/mathlib"@"71150516f28d9826c7341f8815b31f7d8770c212"
+
 /-!
 # Towers of algebras
 

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Johan Commelin <johan@commelin.net>

@@ -156,8 +156,8 @@ instance (priority := 999) subsemiring (U : Subsemiring S) : IsScalarTower U S A
 #align is_scalar_tower.subsemiring IsScalarTower.subsemiring
 
 -- Porting note: @[nolint instance_priority]
-instance of_ring_hom {R A B : Type _} [CommSemiring R] [CommSemiring A] [CommSemiring B]
-    [Algebra R A] [Algebra R B] (f : A →ₐ[R] B) :
+instance (priority := 999) of_ring_hom {R A B : Type _} [CommSemiring R] [CommSemiring A]
+    [CommSemiring B] [Algebra R A] [Algebra R B] (f : A →ₐ[R] B) :
     @IsScalarTower R A B _ f.toRingHom.toAlgebra.toSMul _ :=
   letI := (f : A →+* B).toAlgebra
   of_algebraMap_eq fun x => (f.commutes x).symm

Mathport doesn't understand this, and apparently nor do many of the humans fixing the errors it creates.

If your #align statement complains the def doesn't exist, don't change the #align; work out why it doesn't exist instead.

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -137,17 +137,18 @@ theorem coe_toAlgHom' : (toAlgHom R S A : S → A) = algebraMap S A := rfl
 variable {R S A B}
 
 @[simp]
-theorem AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) : f (algebraMap R A r) = algebraMap R B r :=
+theorem _root_.AlgHom.map_algebraMap (f : A →ₐ[S] B) (r : R) :
+    f (algebraMap R A r) = algebraMap R B r :=
   by rw [algebraMap_apply R S A r, f.commutes, ← algebraMap_apply R S B]
-#align alg_hom.map_algebra_map IsScalarTower.AlgHom.map_algebraMap
+#align alg_hom.map_algebra_map AlgHom.map_algebraMap
 
 variable (R)
 
 @[simp]
-theorem AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
+theorem _root_.AlgHom.comp_algebraMap_of_tower (f : A →ₐ[S] B) :
     (f : A →+* B).comp (algebraMap R A) = algebraMap R B :=
-  RingHom.ext (map_algebraMap f)
-#align alg_hom.comp_algebra_map_of_tower IsScalarTower.AlgHom.comp_algebraMap_of_tower
+  RingHom.ext (AlgHom.map_algebraMap f)
+#align alg_hom.comp_algebra_map_of_tower AlgHom.comp_algebraMap_of_tower
 
 -- conflicts with IsScalarTower.Subalgebra
 instance (priority := 999) subsemiring (U : Subsemiring S) : IsScalarTower U S A :=

@@ -131,8 +131,8 @@ theorem coe_toAlgHom : ↑(toAlgHom R S A) = algebraMap S A :=
 #align is_scalar_tower.coe_to_alg_hom IsScalarTower.coe_toAlgHom
 
 @[simp]
-theorem coe_to_alg_hom' : (toAlgHom R S A : S → A) = algebraMap S A := rfl
-#align is_scalar_tower.coe_to_alg_hom' IsScalarTower.coe_to_alg_hom'
+theorem coe_toAlgHom' : (toAlgHom R S A : S → A) = algebraMap S A := rfl
+#align is_scalar_tower.coe_to_alg_hom' IsScalarTower.coe_toAlgHom'
 
 variable {R S A B}
 
@@ -198,8 +198,8 @@ theorem coe_restrictScalars (f : A →ₐ[S] B) : (f.restrictScalars R : A →+*
 #align alg_hom.coe_restrict_scalars AlgHom.coe_restrictScalars
 
 @[simp]
-theorem coe_restrict_scalars' (f : A →ₐ[S] B) : (restrictScalars R f : A → B) = f := rfl
-#align alg_hom.coe_restrict_scalars' AlgHom.coe_restrict_scalars'
+theorem coe_restrictScalars' (f : A →ₐ[S] B) : (restrictScalars R f : A → B) = f := rfl
+#align alg_hom.coe_restrict_scalars' AlgHom.coe_restrictScalars'
 
 theorem restrictScalars_injective :
     Function.Injective (restrictScalars R : (A →ₐ[S] B) → A →ₐ[R] B) := fun _ _ h =>
@@ -226,8 +226,8 @@ theorem coe_restrictScalars (f : A ≃ₐ[S] B) : (f.restrictScalars R : A ≃+*
 #align alg_equiv.coe_restrict_scalars AlgEquiv.coe_restrictScalars
 
 @[simp]
-theorem coe_restrict_scalars' (f : A ≃ₐ[S] B) : (restrictScalars R f : A → B) = f := rfl
-#align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrict_scalars'
+theorem coe_restrictScalars' (f : A ≃ₐ[S] B) : (restrictScalars R f : A → B) = f := rfl
+#align alg_equiv.coe_restrict_scalars' AlgEquiv.coe_restrictScalars'
 
 theorem restrictScalars_injective :
     Function.Injective (restrictScalars R : (A ≃ₐ[S] B) → A ≃ₐ[R] B) := fun _ _ h =>