algebra.module.localized_module ⟷ Mathlib.Algebra.Module.LocalizedModule

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

@@ -862,10 +862,10 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
   by
   induction' x using LocalizedModule.induction_on with a b
   induction' y using LocalizedModule.induction_on with a' b'
-  simp only [from_localized_module_mk] at eq1 
-  generalize_proofs h1 h2 at eq1 
+  simp only [from_localized_module_mk] at eq1
+  generalize_proofs h1 h2 at eq1
   erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← LinearMap.map_smul,
-    Module.End_algebraMap_isUnit_inv_apply_eq_iff'] at eq1 
+    Module.End_algebraMap_isUnit_inv_apply_eq_iff'] at eq1
   erw [LocalizedModule.mk_eq, ← IsLocalizedModule.eq_iff_exists S f, f.map_smul, f.map_smul, eq1]
   rfl
 #align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.inj
@@ -1216,7 +1216,7 @@ theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [A
   · intro x
     rw [Module.End_isUnit_iff]
     constructor
-    · rintro a b (e : x • a = x • b); simp_rw [Submonoid.smul_def, Algebra.smul_def] at e 
+    · rintro a b (e : x • a = x • b); simp_rw [Submonoid.smul_def, Algebra.smul_def] at e
       exact (h₁ x x.2).hMul_left_cancel e
     · intro a; refine' ⟨((h₁ x x.2).Unit⁻¹ : _) * a, _⟩; change (x : R) • (_ * a) = _
       rw [Algebra.smul_def, ← mul_assoc, IsUnit.mul_val_inv, one_mul]

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

@@ -613,9 +613,9 @@ variable {M M' M'' : Type _} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid
 variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
 #print IsLocalizedModule /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
 /-- The characteristic predicate for localized module.
 `is_localized_module S f` describes that `f : M ⟶ M'` is the localization map identifying `M'` as
 `localized_module S M`.

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

@@ -761,9 +761,9 @@ instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule
     where
   map_units s :=
     ⟨⟨algebraMap R (Module.End R (LocalizedModule S M)) s, LocalizedModule.divBy s,
-        FunLike.ext _ _ <| LocalizedModule.mul_by_divBy s,
-        FunLike.ext _ _ <| LocalizedModule.divBy_mul_by s⟩,
-      FunLike.ext _ _ fun p => p.inductionOn <| by intros; rfl⟩
+        DFunLike.ext _ _ <| LocalizedModule.mul_by_divBy s,
+        DFunLike.ext _ _ <| LocalizedModule.divBy_mul_by s⟩,
+      DFunLike.ext _ _ fun p => p.inductionOn <| by intros; rfl⟩
   surj p :=
     p.inductionOn
       (by

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

@@ -613,9 +613,9 @@ variable {M M' M'' : Type _} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid
 variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
 #print IsLocalizedModule /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
 /-- The characteristic predicate for localized module.
 `is_localized_module S f` describes that `f : M ⟶ M'` is the localization map identifying `M'` as
 `localized_module S M`.

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang, Jujian Zhang
 -/
-import Mathbin.GroupTheory.MonoidLocalization
-import Mathbin.RingTheory.Localization.Basic
-import Mathbin.Algebra.Algebra.RestrictScalars
+import GroupTheory.MonoidLocalization
+import RingTheory.Localization.Basic
+import Algebra.Algebra.RestrictScalars
 
 #align_import algebra.module.localized_module from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
 
@@ -613,9 +613,9 @@ variable {M M' M'' : Type _} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid
 variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
 #print IsLocalizedModule /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
 /-- The characteristic predicate for localized module.
 `is_localized_module S f` describes that `f : M ⟶ M'` is the localization map identifying `M'` as
 `localized_module S M`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

@@ -221,9 +221,9 @@ private theorem add_zero' (x : LocalizedModule S M) : x + 0 = x :=
         exact ⟨1, by rw [one_smul, mul_smul, one_smul]⟩)
     x
 
-#print LocalizedModule.hasNatSmul /-
-instance hasNatSmul : SMul ℕ (LocalizedModule S M) where smul n := nsmulRec n
-#align localized_module.has_nat_smul LocalizedModule.hasNatSmul
+#print LocalizedModule.hasNatSMul /-
+instance hasNatSMul : SMul ℕ (LocalizedModule S M) where smul n := nsmulRec n
+#align localized_module.has_nat_smul LocalizedModule.hasNatSMul
 -/
 
 private theorem nsmul_zero' (x : LocalizedModule S M) : (0 : ℕ) • x = 0 :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -446,7 +446,7 @@ instance isModule : Module (Localization S) (LocalizedModule S M)
     where
   smul := (· • ·)
   one_smul := one_smul'
-  mul_smul := mul_smul'
+  hMul_smul := hMul_smul'
   smul_add := smul_add'
   smul_zero := smul_zero'
   add_smul := add_smul'
@@ -1148,7 +1148,7 @@ theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Modul
 theorem mk'_mul_mk' {M M' : Type _} [Semiring M] [Semiring M'] [Algebra R M] [Algebra R M']
     (f : M →ₐ[R] M') [IsLocalizedModule S f.toLinearMap] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f.toLinearMap m₁ s₁ * mk' f.toLinearMap m₂ s₂ = mk' f.toLinearMap (m₁ * m₂) (s₁ * s₂) :=
-  mk'_mul_mk'_of_map_mul f.toLinearMap f.map_mul m₁ m₂ s₁ s₂
+  mk'_mul_mk'_of_map_mul f.toLinearMap f.map_hMul m₁ m₂ s₁ s₂
 #align is_localized_module.mk'_mul_mk' IsLocalizedModule.mk'_mul_mk'
 -/
 
@@ -1210,14 +1210,14 @@ theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [A
   by
   replace h₃ := fun x =>
     Iff.intro (h₃ x) fun ⟨⟨m, hm⟩, e⟩ =>
-      (h₁ m hm).mul_left_cancel <| by rw [← Algebra.smul_def];
+      (h₁ m hm).hMul_left_cancel <| by rw [← Algebra.smul_def];
         simpa [Submonoid.smul_def] using f.congr_arg e
   constructor
   · intro x
     rw [Module.End_isUnit_iff]
     constructor
     · rintro a b (e : x • a = x • b); simp_rw [Submonoid.smul_def, Algebra.smul_def] at e 
-      exact (h₁ x x.2).mul_left_cancel e
+      exact (h₁ x x.2).hMul_left_cancel e
     · intro a; refine' ⟨((h₁ x x.2).Unit⁻¹ : _) * a, _⟩; change (x : R) • (_ * a) = _
       rw [Algebra.smul_def, ← mul_assoc, IsUnit.mul_val_inv, one_mul]
   · exact h₂

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang, Jujian Zhang
-
-! This file was ported from Lean 3 source module algebra.module.localized_module
-! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.MonoidLocalization
 import Mathbin.RingTheory.Localization.Basic
 import Mathbin.Algebra.Algebra.RestrictScalars
 
+#align_import algebra.module.localized_module from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
+
 /-!
 # Localized Module
 

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

@@ -52,12 +52,15 @@ variable {R : Type u} [CommSemiring R] (S : Submonoid R)
 
 variable (M : Type v) [AddCommMonoid M] [Module R M]
 
+#print LocalizedModule.r /-
 /-- The equivalence relation on `M × S` where `(m1, s1) ≈ (m2, s2)` if and only if
 for some (u : S), u * (s2 • m1 - s1 • m2) = 0-/
 def r (a b : M × S) : Prop :=
   ∃ u : S, u • b.2 • a.1 = u • a.2 • b.1
 #align localized_module.r LocalizedModule.r
+-/
 
+#print LocalizedModule.r.isEquiv /-
 theorem r.isEquiv : IsEquiv _ (r S M) :=
   { refl := fun ⟨m, s⟩ => ⟨1, by rw [one_smul]⟩
     trans := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨m3, s3⟩ ⟨u1, hu1⟩ ⟨u2, hu2⟩ =>
@@ -70,11 +73,14 @@ theorem r.isEquiv : IsEquiv _ (r S M) :=
       rw [hu2', hu1']
     symm := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => ⟨u, hu.symm⟩ }
 #align localized_module.r.is_equiv LocalizedModule.r.isEquiv
+-/
 
+#print LocalizedModule.r.setoid /-
 instance r.setoid : Setoid (M × S) where
   R := r S M
   iseqv := ⟨(r.isEquiv S M).refl, (r.isEquiv S M).symm, (r.isEquiv S M).trans⟩
 #align localized_module.r.setoid LocalizedModule.r.setoid
+-/
 
 -- TODO: change `localization` to use `r'` instead of `r` so that the two types are also defeq,
 -- `localization S = localized_module S R`.
@@ -95,26 +101,35 @@ section
 
 variable {M S}
 
+#print LocalizedModule.mk /-
 /-- The canonical map sending `(m, s) ↦ m/s`-/
 def mk (m : M) (s : S) : LocalizedModule S M :=
   Quotient.mk' ⟨m, s⟩
 #align localized_module.mk LocalizedModule.mk
+-/
 
+#print LocalizedModule.mk_eq /-
 theorem mk_eq {m m' : M} {s s' : S} : mk m s = mk m' s' ↔ ∃ u : S, u • s' • m = u • s • m' :=
   Quotient.eq'
 #align localized_module.mk_eq LocalizedModule.mk_eq
+-/
 
+#print LocalizedModule.induction_on /-
 @[elab_as_elim]
 theorem induction_on {β : LocalizedModule S M → Prop} (h : ∀ (m : M) (s : S), β (mk m s)) :
     ∀ x : LocalizedModule S M, β x := by rintro ⟨⟨m, s⟩⟩; exact h m s
 #align localized_module.induction_on LocalizedModule.induction_on
+-/
 
+#print LocalizedModule.induction_on₂ /-
 @[elab_as_elim]
 theorem induction_on₂ {β : LocalizedModule S M → LocalizedModule S M → Prop}
     (h : ∀ (m m' : M) (s s' : S), β (mk m s) (mk m' s')) : ∀ x y, β x y := by
   rintro ⟨⟨m, s⟩⟩ ⟨⟨m', s'⟩⟩; exact h m m' s s'
 #align localized_module.induction_on₂ LocalizedModule.induction_on₂
+-/
 
+#print LocalizedModule.liftOn /-
 /-- If `f : M × S → α` respects the equivalence relation `localized_module.r`, then
 `f` descents to a map `localized_module M S → α`.
 -/
@@ -122,11 +137,15 @@ def liftOn {α : Type _} (x : LocalizedModule S M) (f : M × S → α)
     (wd : ∀ (p p' : M × S) (h1 : p ≈ p'), f p = f p') : α :=
   Quotient.liftOn x f wd
 #align localized_module.lift_on LocalizedModule.liftOn
+-/
 
+#print LocalizedModule.liftOn_mk /-
 theorem liftOn_mk {α : Type _} {f : M × S → α} (wd : ∀ (p p' : M × S) (h1 : p ≈ p'), f p = f p')
     (m : M) (s : S) : liftOn (mk m s) f wd = f ⟨m, s⟩ := by convert Quotient.liftOn_mk f wd ⟨m, s⟩
 #align localized_module.lift_on_mk LocalizedModule.liftOn_mk
+-/
 
+#print LocalizedModule.liftOn₂ /-
 /-- If `f : M × S → M × S → α` respects the equivalence relation `localized_module.r`, then
 `f` descents to a map `localized_module M S → localized_module M S → α`.
 -/
@@ -134,20 +153,25 @@ def liftOn₂ {α : Type _} (x y : LocalizedModule S M) (f : M × S → M × S 
     (wd : ∀ (p q p' q' : M × S) (h1 : p ≈ p') (h2 : q ≈ q'), f p q = f p' q') : α :=
   Quotient.liftOn₂ x y f wd
 #align localized_module.lift_on₂ LocalizedModule.liftOn₂
+-/
 
+#print LocalizedModule.liftOn₂_mk /-
 theorem liftOn₂_mk {α : Type _} (f : M × S → M × S → α)
     (wd : ∀ (p q p' q' : M × S) (h1 : p ≈ p') (h2 : q ≈ q'), f p q = f p' q') (m m' : M)
     (s s' : S) : liftOn₂ (mk m s) (mk m' s') f wd = f ⟨m, s⟩ ⟨m', s'⟩ := by
   convert Quotient.liftOn₂_mk f wd _ _
 #align localized_module.lift_on₂_mk LocalizedModule.liftOn₂_mk
+-/
 
 instance : Zero (LocalizedModule S M) :=
   ⟨mk 0 1⟩
 
+#print LocalizedModule.zero_mk /-
 @[simp]
 theorem zero_mk (s : S) : mk (0 : M) s = 0 :=
   mk_eq.mpr ⟨1, by rw [one_smul, smul_zero, smul_zero, one_smul]⟩
 #align localized_module.zero_mk LocalizedModule.zero_mk
+-/
 
 instance : Add (LocalizedModule S M)
     where add p1 p2 :=
@@ -163,10 +187,12 @@ instance : Add (LocalizedModule S M)
             hu2' ⊢
           rw [hu1', hu2']⟩
 
+#print LocalizedModule.mk_add_mk /-
 theorem mk_add_mk {m1 m2 : M} {s1 s2 : S} :
     mk m1 s1 + mk m2 s2 = mk (s2 • m1 + s1 • m2) (s1 * s2) :=
   mk_eq.mpr <| ⟨1, by dsimp only <;> rw [one_smul]⟩
 #align localized_module.mk_add_mk LocalizedModule.mk_add_mk
+-/
 
 private theorem add_assoc' (x y z : LocalizedModule S M) : x + y + z = x + (y + z) :=
   by
@@ -239,9 +265,11 @@ instance {M : Type _} [AddCommGroup M] [Module R M] : AddCommGroup (LocalizedMod
       rw [lift_on_mk, mk_add_mk]
       simp }
 
+#print LocalizedModule.mk_neg /-
 theorem mk_neg {M : Type _} [AddCommGroup M] [Module R M] {m : M} {s : S} : mk (-m) s = -mk m s :=
   rfl
 #align localized_module.mk_neg LocalizedModule.mk_neg
+-/
 
 instance {A : Type _} [Semiring A] [Algebra R A] {S : Submonoid R} :
     Semiring (LocalizedModule S A) :=
@@ -326,10 +354,12 @@ instance {A : Type _} [CommRing A] [Algebra R A] {S : Submonoid R} :
       obtain ⟨⟨a₂, s₂⟩, rfl : mk a₂ s₂ = x₂⟩ := Quotient.exists_rep x₂
       exact mk_eq.mpr ⟨1, by simp only [one_smul, mul_comm]⟩ }
 
+#print LocalizedModule.mk_mul_mk /-
 theorem mk_mul_mk {A : Type _} [Semiring A] [Algebra R A] {a₁ a₂ : A} {s₁ s₂ : S} :
     mk a₁ s₁ * mk a₂ s₂ = mk (a₁ * a₂) (s₁ * s₂) :=
   rfl
 #align localized_module.mk_mul_mk LocalizedModule.mk_mul_mk
+-/
 
 instance : SMul (Localization S) (LocalizedModule S M)
     where smul f x :=
@@ -354,11 +384,13 @@ instance : SMul (Localization S) (LocalizedModule S M)
         ring_nf at eq1' ⊢
         rw [eq1'])
 
+#print LocalizedModule.mk_smul_mk /-
 theorem mk_smul_mk (r : R) (m : M) (s t : S) : Localization.mk r s • mk m t = mk (r • m) (s * t) :=
   by
   unfold SMul.smul
   rw [Localization.liftOn_mk, lift_on_mk]
 #align localized_module.mk_smul_mk LocalizedModule.mk_smul_mk
+-/
 
 private theorem one_smul' (m : LocalizedModule S M) : (1 : Localization S) • m = m :=
   by
@@ -412,6 +444,7 @@ private theorem zero_smul' (x : LocalizedModule S M) : (0 : Localization S) •
   induction' x using LocalizedModule.induction_on with m s
   rw [← Localization.mk_zero s, mk_smul_mk, zero_smul, zero_mk]
 
+#print LocalizedModule.isModule /-
 instance isModule : Module (Localization S) (LocalizedModule S M)
     where
   smul := (· • ·)
@@ -422,29 +455,40 @@ instance isModule : Module (Localization S) (LocalizedModule S M)
   add_smul := add_smul'
   zero_smul := zero_smul'
 #align localized_module.is_module LocalizedModule.isModule
+-/
 
+#print LocalizedModule.mk_cancel_common_left /-
 @[simp]
 theorem mk_cancel_common_left (s' s : S) (m : M) : mk (s' • m) (s' * s) = mk m s :=
   mk_eq.mpr ⟨1, by simp only [mul_smul, one_smul]; rw [smul_comm]⟩
 #align localized_module.mk_cancel_common_left LocalizedModule.mk_cancel_common_left
+-/
 
+#print LocalizedModule.mk_cancel /-
 @[simp]
 theorem mk_cancel (s : S) (m : M) : mk (s • m) s = mk m 1 :=
   mk_eq.mpr ⟨1, by simp⟩
 #align localized_module.mk_cancel LocalizedModule.mk_cancel
+-/
 
+#print LocalizedModule.mk_cancel_common_right /-
 @[simp]
 theorem mk_cancel_common_right (s s' : S) (m : M) : mk (s' • m) (s * s') = mk m s :=
   mk_eq.mpr ⟨1, by simp [mul_smul]⟩
 #align localized_module.mk_cancel_common_right LocalizedModule.mk_cancel_common_right
+-/
 
+#print LocalizedModule.isModule' /-
 instance isModule' : Module R (LocalizedModule S M) :=
   { Module.compHom (LocalizedModule S M) <| algebraMap R (Localization S) with }
 #align localized_module.is_module' LocalizedModule.isModule'
+-/
 
+#print LocalizedModule.smul'_mk /-
 theorem smul'_mk (r : R) (s : S) (m : M) : r • mk m s = mk (r • m) s := by
   erw [mk_smul_mk r m 1 s, one_mul]
 #align localized_module.smul'_mk LocalizedModule.smul'_mk
+-/
 
 instance {A : Type _} [Semiring A] [Algebra R A] : Algebra (Localization S) (LocalizedModule S A) :=
   Algebra.ofModule
@@ -463,6 +507,7 @@ instance {A : Type _} [Semiring A] [Algebra R A] : Algebra (Localization S) (Loc
       rw [mk_mul_mk, ← Localization.mk_eq_mk', mk_smul_mk, mk_smul_mk, mk_mul_mk, mul_left_comm,
         mul_smul_comm])
 
+#print LocalizedModule.algebraMap_mk /-
 theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
     algebraMap _ _ (Localization.mk a s) = mk (algebraMap R A a) s :=
   by
@@ -470,10 +515,12 @@ theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
   change _ • mk _ _ = _
   rw [mk_smul_mk, Algebra.algebraMap_eq_smul_one, mul_one]
 #align localized_module.algebra_map_mk LocalizedModule.algebraMap_mk
+-/
 
 instance : IsScalarTower R (Localization S) (LocalizedModule S M) :=
   RestrictScalars.isScalarTower R (Localization S) (LocalizedModule S M)
 
+#print LocalizedModule.algebra' /-
 instance algebra' {A : Type _} [Semiring A] [Algebra R A] : Algebra R (LocalizedModule S A) :=
   { (algebraMap (Localization S) (LocalizedModule S A)).comp (algebraMap R <| Localization S),
     show Module R (LocalizedModule S A) by
@@ -491,11 +538,13 @@ instance algebra' {A : Type _} [Semiring A] [Algebra R A] : Algebra R (Localized
       rw [← Localization.mk_one_eq_algebraMap, algebra_map_mk, mk_mul_mk, smul'_mk,
         Algebra.smul_def, one_mul] }
 #align localized_module.algebra' LocalizedModule.algebra'
+-/
 
 section
 
 variable (S M)
 
+#print LocalizedModule.mkLinearMap /-
 /-- The function `m ↦ m / 1` as an `R`-linear map.
 -/
 @[simps]
@@ -505,9 +554,11 @@ def mkLinearMap : M →ₗ[R] LocalizedModule S M
   map_add' x y := by simp [mk_add_mk]
   map_smul' r x := (smul'_mk _ _ _).symm
 #align localized_module.mk_linear_map LocalizedModule.mkLinearMap
+-/
 
 end
 
+#print LocalizedModule.divBy /-
 /-- For any `s : S`, there is an `R`-linear map given by `a/b ↦ a/(b*s)`.
 -/
 @[simps]
@@ -526,7 +577,9 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M
       y
   map_smul' r x := x.inductionOn <| by intros; simp [LocalizedModule.liftOn_mk, smul'_mk]
 #align localized_module.div_by LocalizedModule.divBy
+-/
 
+#print LocalizedModule.divBy_mul_by /-
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
     divBy s (algebraMap R (Module.End R (LocalizedModule S M)) s p) = p :=
   p.inductionOn
@@ -535,7 +588,9 @@ theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
       simp only [LocalizedModule.liftOn_mk, Module.algebraMap_end_apply, smul'_mk, div_by_apply]
       erw [mk_cancel_common_left s t])
 #align localized_module.div_by_mul_by LocalizedModule.divBy_mul_by
+-/
 
+#print LocalizedModule.mul_by_divBy /-
 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
     algebraMap R (Module.End R (LocalizedModule S M)) s (divBy s p) = p :=
   p.inductionOn
@@ -544,6 +599,7 @@ theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
       simp only [LocalizedModule.liftOn_mk, div_by_apply, Module.algebraMap_end_apply, smul'_mk]
       erw [mk_cancel_common_left s t])
 #align localized_module.mul_by_div_by LocalizedModule.mul_by_divBy
+-/
 
 end
 
@@ -560,9 +616,9 @@ variable {M M' M'' : Type _} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid
 variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
 #print IsLocalizedModule /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
 /-- The characteristic predicate for localized module.
 `is_localized_module S f` describes that `f : M ⟶ M'` is the localization map identifying `M'` as
 `localized_module S M`.
@@ -576,6 +632,7 @@ class IsLocalizedModule : Prop where
 
 namespace LocalizedModule
 
+#print LocalizedModule.lift' /-
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 there is a linear map `localized_module S M → M''`.
@@ -604,12 +661,16 @@ noncomputable def lift' (g : M →ₗ[R] M'')
       g.map_smul, eq1]
     rfl
 #align localized_module.lift' LocalizedModule.lift'
+-/
 
+#print LocalizedModule.lift'_mk /-
 theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (m : M) (s : S) : LocalizedModule.lift' S g h (LocalizedModule.mk m s) = (h s).Unit⁻¹.1 (g m) :=
   rfl
 #align localized_module.lift'_mk LocalizedModule.lift'_mk
+-/
 
+#print LocalizedModule.lift'_add /-
 theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (x y) :
     LocalizedModule.lift' S g h (x + y) =
@@ -626,7 +687,9 @@ theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
       erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, mul_comm, mul_smul, ← map_smul]; rfl)
     x y
 #align localized_module.lift'_add LocalizedModule.lift'_add
+-/
 
+#print LocalizedModule.lift'_smul /-
 theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (r : R) (m) : r • LocalizedModule.lift' S g h m = LocalizedModule.lift' S g h (r • m) :=
   m.inductionOn
@@ -636,7 +699,9 @@ theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (
       generalize_proofs h1 h2
       erw [← h1.unit⁻¹.1.map_smul, ← g.map_smul])
 #align localized_module.lift'_smul LocalizedModule.lift'_smul
+-/
 
+#print LocalizedModule.lift /-
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 there is a linear map `localized_module S M → M''`.
@@ -648,7 +713,9 @@ noncomputable def lift (g : M →ₗ[R] M'')
   map_add' := LocalizedModule.lift'_add S g h
   map_smul' r x := by rw [LocalizedModule.lift'_smul, RingHom.id_apply]
 #align localized_module.lift LocalizedModule.lift
+-/
 
+#print LocalizedModule.lift_mk /-
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 `lift g m s = s⁻¹ • g m`.
@@ -657,7 +724,9 @@ theorem lift_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Mod
     (m : M) (s : S) : LocalizedModule.lift S g h (LocalizedModule.mk m s) = (h s).Unit⁻¹.1 (g m) :=
   rfl
 #align localized_module.lift_mk LocalizedModule.lift_mk
+-/
 
+#print LocalizedModule.lift_comp /-
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 there is a linear map `lift g ∘ mk_linear_map = g`.
@@ -668,7 +737,9 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
   ext x; dsimp; rw [LocalizedModule.lift_mk]
   erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, one_smul]
 #align localized_module.lift_comp LocalizedModule.lift_comp
+-/
 
+#print LocalizedModule.lift_unique /-
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible and
 `l` is another linear map `localized_module S M ⟶ M''` such that `l ∘ mk_linear_map = g` then
@@ -684,9 +755,11 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
   congr 1; rw [LocalizedModule.mk_eq]
   refine' ⟨1, _⟩; simp only [one_smul]; rfl
 #align localized_module.lift_unique LocalizedModule.lift_unique
+-/
 
 end LocalizedModule
 
+#print localizedModuleIsLocalizedModule /-
 instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule.mkLinearMap S M)
     where
   map_units s :=
@@ -706,6 +779,7 @@ instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule
       mpr := fun ⟨c, eq1⟩ =>
         LocalizedModule.mk_eq.mpr ⟨c, by simpa only [eq_comm, one_smul] using eq1⟩ }
 #align localized_module_is_localized_module localizedModuleIsLocalizedModule
+-/
 
 namespace IsLocalizedModule
 
@@ -727,13 +801,16 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
 #align is_localized_module.from_localized_module' IsLocalizedModule.fromLocalizedModule'
 -/
 
+#print IsLocalizedModule.fromLocalizedModule'_mk /-
 @[simp]
 theorem fromLocalizedModule'_mk (m : M) (s : S) :
     fromLocalizedModule' S f (LocalizedModule.mk m s) =
       (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
   rfl
 #align is_localized_module.from_localized_module'_mk IsLocalizedModule.fromLocalizedModule'_mk
+-/
 
+#print IsLocalizedModule.fromLocalizedModule'_add /-
 theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
     fromLocalizedModule' S f (x + y) = fromLocalizedModule' S f x + fromLocalizedModule' S f y :=
   LocalizedModule.induction_on₂
@@ -749,7 +826,9 @@ theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
       · dsimp; erw [mul_comm, f.map_smul, mul_smul]; rfl)
     x y
 #align is_localized_module.from_localized_module'_add IsLocalizedModule.fromLocalizedModule'_add
+-/
 
+#print IsLocalizedModule.fromLocalizedModule'_smul /-
 theorem fromLocalizedModule'_smul (r : R) (x : LocalizedModule S M) :
     r • fromLocalizedModule' S f x = fromLocalizedModule' S f (r • x) :=
   LocalizedModule.induction_on
@@ -759,7 +838,9 @@ theorem fromLocalizedModule'_smul (r : R) (x : LocalizedModule S M) :
       generalize_proofs h1; erw [f.map_smul, h1.unit⁻¹.1.map_smul]; rfl)
     x
 #align is_localized_module.from_localized_module'_smul IsLocalizedModule.fromLocalizedModule'_smul
+-/
 
+#print IsLocalizedModule.fromLocalizedModule /-
 /-- If `(M', f : M ⟶ M')` satisfies universal property of localized module, there is a canonical map
 `localized_module S M ⟶ M'`.
 -/
@@ -769,13 +850,17 @@ noncomputable def fromLocalizedModule : LocalizedModule S M →ₗ[R] M'
   map_add' := fromLocalizedModule'_add S f
   map_smul' r x := by rw [from_localized_module'_smul, RingHom.id_apply]
 #align is_localized_module.from_localized_module IsLocalizedModule.fromLocalizedModule
+-/
 
+#print IsLocalizedModule.fromLocalizedModule_mk /-
 theorem fromLocalizedModule_mk (m : M) (s : S) :
     fromLocalizedModule S f (LocalizedModule.mk m s) =
       (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
   rfl
 #align is_localized_module.from_localized_module_mk IsLocalizedModule.fromLocalizedModule_mk
+-/
 
+#print IsLocalizedModule.fromLocalizedModule.inj /-
 theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f := fun x y eq1 =>
   by
   induction' x using LocalizedModule.induction_on with a b
@@ -787,17 +872,23 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
   erw [LocalizedModule.mk_eq, ← IsLocalizedModule.eq_iff_exists S f, f.map_smul, f.map_smul, eq1]
   rfl
 #align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.inj
+-/
 
+#print IsLocalizedModule.fromLocalizedModule.surj /-
 theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S f := fun x =>
   let ⟨⟨m, s⟩, eq1⟩ := IsLocalizedModule.surj S f x
   ⟨LocalizedModule.mk m s, by
     rw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← eq1]; rfl⟩
 #align is_localized_module.from_localized_module.surj IsLocalizedModule.fromLocalizedModule.surj
+-/
 
+#print IsLocalizedModule.fromLocalizedModule.bij /-
 theorem fromLocalizedModule.bij : Function.Bijective <| fromLocalizedModule S f :=
   ⟨fromLocalizedModule.inj _ _, fromLocalizedModule.surj _ _⟩
 #align is_localized_module.from_localized_module.bij IsLocalizedModule.fromLocalizedModule.bij
+-/
 
+#print IsLocalizedModule.iso /-
 /--
 If `(M', f : M ⟶ M')` satisfies universal property of localized module, then `M'` is isomorphic to
 `localized_module S M` as an `R`-module.
@@ -807,12 +898,16 @@ noncomputable def iso : LocalizedModule S M ≃ₗ[R] M' :=
   { fromLocalizedModule S f,
     Equiv.ofBijective (fromLocalizedModule S f) <| fromLocalizedModule.bij _ _ with }
 #align is_localized_module.iso IsLocalizedModule.iso
+-/
 
+#print IsLocalizedModule.iso_apply_mk /-
 theorem iso_apply_mk (m : M) (s : S) :
     iso S f (LocalizedModule.mk m s) = (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
   rfl
 #align is_localized_module.iso_apply_mk IsLocalizedModule.iso_apply_mk
+-/
 
+#print IsLocalizedModule.iso_symm_apply_aux /-
 theorem iso_symm_apply_aux (m : M') :
     (iso S f).symm m =
       LocalizedModule.mk (IsLocalizedModule.surj S f m).some.1
@@ -824,7 +919,9 @@ theorem iso_symm_apply_aux (m : M') :
   simp only [iso_apply, LinearMap.toFun_eq_coe, from_localized_module_mk]
   erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff', h2.some_spec]
 #align is_localized_module.iso_symm_apply_aux IsLocalizedModule.iso_symm_apply_aux
+-/
 
+#print IsLocalizedModule.iso_symm_apply' /-
 theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
     (iso S f).symm m = LocalizedModule.mk a b :=
   (iso_symm_apply_aux S f m).trans <|
@@ -833,13 +930,17 @@ theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
       erw [← IsLocalizedModule.eq_iff_exists S f, f.map_smul, f.map_smul, ← h1.some_spec, ←
         mul_smul, mul_comm, mul_smul, eq1]
 #align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'
+-/
 
+#print IsLocalizedModule.iso_symm_comp /-
 theorem iso_symm_comp : (iso S f).symm.toLinearMap.comp f = LocalizedModule.mkLinearMap S M :=
   by
   ext m; rw [LinearMap.comp_apply, LocalizedModule.mkLinearMap_apply]
   change (iso S f).symm _ = _; rw [iso_symm_apply']; exact one_smul _ _
 #align is_localized_module.iso_symm_comp IsLocalizedModule.iso_symm_comp
+-/
 
+#print IsLocalizedModule.lift /-
 /--
 If `M'` is a localized module and `g` is a linear map `M' → M''` such that all scalar multiplication
 by `s : S` is invertible, then there is a linear map `M' → M''`.
@@ -848,7 +949,9 @@ noncomputable def lift (g : M →ₗ[R] M'')
     (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x)) : M' →ₗ[R] M'' :=
   (LocalizedModule.lift S g h).comp (iso S f).symm.toLinearMap
 #align is_localized_module.lift IsLocalizedModule.lift
+-/
 
+#print IsLocalizedModule.lift_comp /-
 theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x)) :
     (lift S f g h).comp f = g :=
   by
@@ -857,7 +960,9 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
   convert LocalizedModule.lift_comp S g h
   exact iso_symm_comp _ _
 #align is_localized_module.lift_comp IsLocalizedModule.lift_comp
+-/
 
+#print IsLocalizedModule.lift_unique /-
 theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (l : M' →ₗ[R] M'') (hl : l.comp f = g) : lift S f g h = l :=
   by
@@ -869,7 +974,9 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
   · rw [LinearMap.comp_assoc, ← hl]; congr 1; ext x
     erw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, one_smul]
 #align is_localized_module.lift_unique IsLocalizedModule.lift_unique
+-/
 
+#print IsLocalizedModule.is_universal /-
 /-- Universal property from localized module:
 If `(M', f : M ⟶ M')` is a localized module then it satisfies the following universal property:
 For every `R`-module `M''` which every `s : S`-scalar multiplication is invertible and for every
@@ -889,11 +996,14 @@ theorem is_universal :
       ∃! l : M' →ₗ[R] M'', l.comp f = g :=
   fun g h => ⟨lift S f g h, lift_comp S f g h, fun l hl => (lift_unique S f g h l hl).symm⟩
 #align is_localized_module.is_universal IsLocalizedModule.is_universal
+-/
 
+#print IsLocalizedModule.ringHom_ext /-
 theorem ringHom_ext (map_unit : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     ⦃j k : M' →ₗ[R] M''⦄ (h : j.comp f = k.comp f) : j = k := by
   rw [← lift_unique S f (k.comp f) map_unit j h, lift_unique]; rfl
 #align is_localized_module.ring_hom_ext IsLocalizedModule.ringHom_ext
+-/
 
 #print IsLocalizedModule.linearEquiv /-
 /-- If `(M', f)` and `(M'', g)` both satisfy universal property of localized module, then `M', M''`
@@ -906,66 +1016,91 @@ noncomputable def linearEquiv [IsLocalizedModule S g] : M' ≃ₗ[R] M'' :=
 
 variable {S}
 
+#print IsLocalizedModule.smul_injective /-
 theorem smul_injective (s : S) : Function.Injective fun m : M' => s • m :=
   ((Module.End_isUnit_iff _).mp (IsLocalizedModule.map_units f s)).Injective
 #align is_localized_module.smul_injective IsLocalizedModule.smul_injective
+-/
 
+#print IsLocalizedModule.smul_inj /-
 theorem smul_inj (s : S) (m₁ m₂ : M') : s • m₁ = s • m₂ ↔ m₁ = m₂ :=
   (smul_injective f s).eq_iff
 #align is_localized_module.smul_inj IsLocalizedModule.smul_inj
+-/
 
+#print IsLocalizedModule.mk' /-
 /-- `mk' f m s` is the fraction `m/s` with respect to the localization map `f`. -/
 noncomputable def mk' (m : M) (s : S) : M' :=
   fromLocalizedModule S f (LocalizedModule.mk m s)
 #align is_localized_module.mk' IsLocalizedModule.mk'
+-/
 
+#print IsLocalizedModule.mk'_smul /-
 theorem mk'_smul (r : R) (m : M) (s : S) : mk' f (r • m) s = r • mk' f m s := by delta mk';
   rw [← LocalizedModule.smul'_mk, LinearMap.map_smul]
 #align is_localized_module.mk'_smul IsLocalizedModule.mk'_smul
+-/
 
+#print IsLocalizedModule.mk'_add_mk' /-
 theorem mk'_add_mk' (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ + mk' f m₂ s₂ = mk' f (s₂ • m₁ + s₁ • m₂) (s₁ * s₂) := by delta mk';
   rw [← map_add, LocalizedModule.mk_add_mk]
 #align is_localized_module.mk'_add_mk' IsLocalizedModule.mk'_add_mk'
+-/
 
+#print IsLocalizedModule.mk'_zero /-
 @[simp]
 theorem mk'_zero (s : S) : mk' f 0 s = 0 := by rw [← zero_smul R (0 : M), mk'_smul, zero_smul]
 #align is_localized_module.mk'_zero IsLocalizedModule.mk'_zero
+-/
 
 variable (S)
 
+#print IsLocalizedModule.mk'_one /-
 @[simp]
 theorem mk'_one (m : M) : mk' f m (1 : S) = f m := by delta mk';
   rw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, Submonoid.coe_one,
     one_smul]
 #align is_localized_module.mk'_one IsLocalizedModule.mk'_one
+-/
 
 variable {S}
 
+#print IsLocalizedModule.mk'_cancel /-
 @[simp]
 theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m := by delta mk';
   rw [LocalizedModule.mk_cancel, ← mk'_one S f]; rfl
 #align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancel
+-/
 
+#print IsLocalizedModule.mk'_cancel' /-
 @[simp]
 theorem mk'_cancel' (m : M) (s : S) : s • mk' f m s = f m := by
   rw [Submonoid.smul_def, ← mk'_smul, ← Submonoid.smul_def, mk'_cancel]
 #align is_localized_module.mk'_cancel' IsLocalizedModule.mk'_cancel'
+-/
 
+#print IsLocalizedModule.mk'_cancel_left /-
 @[simp]
 theorem mk'_cancel_left (m : M) (s₁ s₂ : S) : mk' f (s₁ • m) (s₁ * s₂) = mk' f m s₂ := by delta mk';
   rw [LocalizedModule.mk_cancel_common_left]
 #align is_localized_module.mk'_cancel_left IsLocalizedModule.mk'_cancel_left
+-/
 
+#print IsLocalizedModule.mk'_cancel_right /-
 @[simp]
 theorem mk'_cancel_right (m : M) (s₁ s₂ : S) : mk' f (s₂ • m) (s₁ * s₂) = mk' f m s₁ := by
   delta mk'; rw [LocalizedModule.mk_cancel_common_right]
 #align is_localized_module.mk'_cancel_right IsLocalizedModule.mk'_cancel_right
+-/
 
+#print IsLocalizedModule.mk'_add /-
 theorem mk'_add (m₁ m₂ : M) (s : S) : mk' f (m₁ + m₂) s = mk' f m₁ s + mk' f m₂ s := by
   rw [mk'_add_mk', ← smul_add, mk'_cancel_left]
 #align is_localized_module.mk'_add IsLocalizedModule.mk'_add
+-/
 
+#print IsLocalizedModule.mk'_eq_mk'_iff /-
 theorem mk'_eq_mk'_iff (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ = mk' f m₂ s₂ ↔ ∃ s : S, s • s₁ • m₂ = s • s₂ • m₁ :=
   by
@@ -973,24 +1108,32 @@ theorem mk'_eq_mk'_iff (m₁ m₂ : M) (s₁ s₂ : S) :
   rw [(from_localized_module.inj S f).eq_iff, LocalizedModule.mk_eq]
   simp_rw [eq_comm]
 #align is_localized_module.mk'_eq_mk'_iff IsLocalizedModule.mk'_eq_mk'_iff
+-/
 
+#print IsLocalizedModule.mk'_neg /-
 theorem mk'_neg {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m : M) (s : S) : mk' f (-m) s = -mk' f m s := by
   delta mk'; rw [LocalizedModule.mk_neg, map_neg]
 #align is_localized_module.mk'_neg IsLocalizedModule.mk'_neg
+-/
 
+#print IsLocalizedModule.mk'_sub /-
 theorem mk'_sub {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m₁ m₂ : M) (s : S) :
     mk' f (m₁ - m₂) s = mk' f m₁ s - mk' f m₂ s := by
   rw [sub_eq_add_neg, sub_eq_add_neg, mk'_add, mk'_neg]
 #align is_localized_module.mk'_sub IsLocalizedModule.mk'_sub
+-/
 
+#print IsLocalizedModule.mk'_sub_mk' /-
 theorem mk'_sub_mk' {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ - mk' f m₂ s₂ = mk' f (s₂ • m₁ - s₁ • m₂) (s₁ * s₂) := by
   rw [sub_eq_add_neg, ← mk'_neg, mk'_add_mk', smul_neg, ← sub_eq_add_neg]
 #align is_localized_module.mk'_sub_mk' IsLocalizedModule.mk'_sub_mk'
+-/
 
+#print IsLocalizedModule.mk'_mul_mk'_of_map_mul /-
 theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Module R M]
     [Algebra R M'] (f : M →ₗ[R] M') (hf : ∀ m₁ m₂, f (m₁ * m₂) = f m₁ * f m₂)
     [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
@@ -1002,51 +1145,67 @@ theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Modul
   rw [smul_smul_smul_comm, ← mk'_smul, ← mk'_smul]
   simp_rw [← Submonoid.smul_def, mk'_cancel, smul_eq_mul, hf]
 #align is_localized_module.mk'_mul_mk'_of_map_mul IsLocalizedModule.mk'_mul_mk'_of_map_mul
+-/
 
+#print IsLocalizedModule.mk'_mul_mk' /-
 theorem mk'_mul_mk' {M M' : Type _} [Semiring M] [Semiring M'] [Algebra R M] [Algebra R M']
     (f : M →ₐ[R] M') [IsLocalizedModule S f.toLinearMap] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f.toLinearMap m₁ s₁ * mk' f.toLinearMap m₂ s₂ = mk' f.toLinearMap (m₁ * m₂) (s₁ * s₂) :=
   mk'_mul_mk'_of_map_mul f.toLinearMap f.map_mul m₁ m₂ s₁ s₂
 #align is_localized_module.mk'_mul_mk' IsLocalizedModule.mk'_mul_mk'
+-/
 
 variable {f}
 
+#print IsLocalizedModule.mk'_eq_iff /-
 @[simp]
 theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m' := by
   rw [← smul_inj f s, Submonoid.smul_def, ← mk'_smul, ← Submonoid.smul_def, mk'_cancel]
 #align is_localized_module.mk'_eq_iff IsLocalizedModule.mk'_eq_iff
+-/
 
+#print IsLocalizedModule.mk'_eq_zero /-
 @[simp]
 theorem mk'_eq_zero {m : M} (s : S) : mk' f m s = 0 ↔ f m = 0 := by rw [mk'_eq_iff, smul_zero]
 #align is_localized_module.mk'_eq_zero IsLocalizedModule.mk'_eq_zero
+-/
 
 variable (f)
 
+#print IsLocalizedModule.mk'_eq_zero' /-
 theorem mk'_eq_zero' {m : M} (s : S) : mk' f m s = 0 ↔ ∃ s' : S, s' • m = 0 := by
   simp_rw [← mk'_zero f (1 : S), mk'_eq_mk'_iff, smul_zero, one_smul, eq_comm]
 #align is_localized_module.mk'_eq_zero' IsLocalizedModule.mk'_eq_zero'
+-/
 
+#print IsLocalizedModule.mk_eq_mk' /-
 theorem mk_eq_mk' (s : S) (m : M) :
     LocalizedModule.mk m s = mk' (LocalizedModule.mkLinearMap S M) m s := by
   rw [eq_comm, mk'_eq_iff, Submonoid.smul_def, LocalizedModule.smul'_mk, ← Submonoid.smul_def,
     LocalizedModule.mk_cancel, LocalizedModule.mkLinearMap_apply]
 #align is_localized_module.mk_eq_mk' IsLocalizedModule.mk_eq_mk'
+-/
 
 variable (S)
 
+#print IsLocalizedModule.eq_zero_iff /-
 theorem eq_zero_iff {m : M} : f m = 0 ↔ ∃ s' : S, s' • m = 0 :=
   (mk'_eq_zero (1 : S)).symm.trans (mk'_eq_zero' f _)
 #align is_localized_module.eq_zero_iff IsLocalizedModule.eq_zero_iff
+-/
 
+#print IsLocalizedModule.mk'_surjective /-
 theorem mk'_surjective : Function.Surjective (Function.uncurry <| mk' f : M × S → M') :=
   by
   intro x
   obtain ⟨⟨m, s⟩, e : s • x = f m⟩ := IsLocalizedModule.surj S f x
   exact ⟨⟨m, s⟩, mk'_eq_iff.mpr e.symm⟩
 #align is_localized_module.mk'_surjective IsLocalizedModule.mk'_surjective
+-/
 
 section Algebra
 
+#print IsLocalizedModule.mkOfAlgebra /-
 theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [Algebra R S]
     [Algebra R S'] (M : Submonoid R) (f : S →ₐ[R] S') (h₁ : ∀ x ∈ M, IsUnit (algebraMap R S' x))
     (h₂ : ∀ y, ∃ x : S × M, x.2 • y = f x.1) (h₃ : ∀ x, f x = 0 → ∃ m : M, m • x = 0) :
@@ -1067,6 +1226,7 @@ theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [A
   · exact h₂
   · intros; dsimp; rw [eq_comm, ← sub_eq_zero, ← map_sub, h₃]; simp_rw [smul_sub, sub_eq_zero]
 #align is_localized_module.mk_of_algebra IsLocalizedModule.mkOfAlgebra
+-/
 
 end Algebra
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -351,7 +351,7 @@ instance : SMul (Localization S) (LocalizedModule S M)
         use u
         have eq1' := congr_arg (· • t • m) eq1
         simp only [← mul_smul, smul_assoc, Submonoid.smul_def, Submonoid.coe_mul] at eq1' ⊢
-        ring_nf  at eq1' ⊢
+        ring_nf at eq1' ⊢
         rw [eq1'])
 
 theorem mk_smul_mk (r : R) (m : M) (s t : S) : Localization.mk r s • mk m t = mk (r • m) (s * t) :=
@@ -560,9 +560,9 @@ variable {M M' M'' : Type _} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid
 variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
 #print IsLocalizedModule /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
 /-- The characteristic predicate for localized module.
 `is_localized_module S f` describes that `f : M ⟶ M'` is the localization map identifying `M'` as
 `localized_module S M`.
@@ -781,7 +781,7 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
   induction' x using LocalizedModule.induction_on with a b
   induction' y using LocalizedModule.induction_on with a' b'
   simp only [from_localized_module_mk] at eq1 
-  generalize_proofs h1 h2  at eq1 
+  generalize_proofs h1 h2 at eq1 
   erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← LinearMap.map_smul,
     Module.End_algebraMap_isUnit_inv_apply_eq_iff'] at eq1 
   erw [LocalizedModule.mk_eq, ← IsLocalizedModule.eq_iff_exists S f, f.map_smul, f.map_smul, eq1]

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

@@ -66,7 +66,7 @@ theorem r.isEquiv : IsEquiv _ (r S M) :=
       -- Put everything in the same shape, sorting the terms using `simp`
       have hu1' := congr_arg ((· • ·) (u2 * s3)) hu1.symm
       have hu2' := congr_arg ((· • ·) (u1 * s1)) hu2.symm
-      simp only [← mul_smul, smul_assoc, mul_assoc, mul_comm, mul_left_comm] at hu1' hu2'⊢
+      simp only [← mul_smul, smul_assoc, mul_assoc, mul_comm, mul_left_comm] at hu1' hu2' ⊢
       rw [hu2', hu1']
     symm := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => ⟨u, hu.symm⟩ }
 #align localized_module.r.is_equiv LocalizedModule.r.isEquiv
@@ -159,8 +159,8 @@ instance : Add (LocalizedModule S M)
           -- Put everything in the same shape, sorting the terms using `simp`
           have hu1' := congr_arg ((· • ·) (u2 * s2 * s2')) hu1
           have hu2' := congr_arg ((· • ·) (u1 * s1 * s1')) hu2
-          simp only [smul_add, ← mul_smul, smul_assoc, mul_assoc, mul_comm, mul_left_comm] at
-            hu1' hu2'⊢
+          simp only [smul_add, ← mul_smul, smul_assoc, mul_assoc, mul_comm, mul_left_comm] at hu1'
+            hu2' ⊢
           rw [hu1', hu2']⟩
 
 theorem mk_add_mk {m1 m2 : M} {s1 s2 : S} :
@@ -254,7 +254,7 @@ instance {A : Type _} [Semiring A] [Algebra R A] {S : Submonoid R} :
           rintro ⟨a₁, s₁⟩ ⟨a₂, s₂⟩ ⟨b₁, t₁⟩ ⟨b₂, t₂⟩ ⟨u₁, e₁⟩ ⟨u₂, e₂⟩
           rw [mk_eq]
           use u₁ * u₂
-          dsimp only at e₁ e₂⊢
+          dsimp only at e₁ e₂ ⊢
           rw [eq_comm]
           trans (u₁ • t₁ • a₁) • u₂ • t₂ • a₂
           rw [e₁, e₂]; swap; rw [eq_comm]
@@ -341,7 +341,7 @@ instance : SMul (Localization S) (LocalizedModule S M)
             refine' mk_eq.mpr ⟨u, _⟩
             have h' := congr_arg ((· • ·) (s • r)) h
             simp only [← mul_smul, smul_assoc, mul_comm, mul_left_comm, Submonoid.smul_def,
-              Submonoid.coe_mul] at h'⊢
+              Submonoid.coe_mul] at h' ⊢
             rw [h']))
       (by
         induction' x using LocalizedModule.induction_on with m t
@@ -350,8 +350,8 @@ instance : SMul (Localization S) (LocalizedModule S M)
         obtain ⟨u, eq1⟩ := localization.r_iff_exists.mp h
         use u
         have eq1' := congr_arg (· • t • m) eq1
-        simp only [← mul_smul, smul_assoc, Submonoid.smul_def, Submonoid.coe_mul] at eq1'⊢
-        ring_nf  at eq1'⊢
+        simp only [← mul_smul, smul_assoc, Submonoid.smul_def, Submonoid.coe_mul] at eq1' ⊢
+        ring_nf  at eq1' ⊢
         rw [eq1'])
 
 theorem mk_smul_mk (r : R) (m : M) (s t : S) : Localization.mk r s • mk m t = mk (r • m) (s * t) :=
@@ -524,7 +524,7 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M
           mk_cancel_common_left s]
         rw [show s * (t₁ * t₂) = t₁ * (s * t₂) by ext; simp only [Submonoid.coe_mul]; ring])
       y
-  map_smul' r x := x.inductionOn <| by intros ; simp [LocalizedModule.liftOn_mk, smul'_mk]
+  map_smul' r x := x.inductionOn <| by intros; simp [LocalizedModule.liftOn_mk, smul'_mk]
 #align localized_module.div_by LocalizedModule.divBy
 
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
@@ -693,7 +693,7 @@ instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule
     ⟨⟨algebraMap R (Module.End R (LocalizedModule S M)) s, LocalizedModule.divBy s,
         FunLike.ext _ _ <| LocalizedModule.mul_by_divBy s,
         FunLike.ext _ _ <| LocalizedModule.divBy_mul_by s⟩,
-      FunLike.ext _ _ fun p => p.inductionOn <| by intros ; rfl⟩
+      FunLike.ext _ _ fun p => p.inductionOn <| by intros; rfl⟩
   surj p :=
     p.inductionOn
       (by
@@ -780,10 +780,10 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
   by
   induction' x using LocalizedModule.induction_on with a b
   induction' y using LocalizedModule.induction_on with a' b'
-  simp only [from_localized_module_mk] at eq1
-  generalize_proofs h1 h2  at eq1
+  simp only [from_localized_module_mk] at eq1 
+  generalize_proofs h1 h2  at eq1 
   erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← LinearMap.map_smul,
-    Module.End_algebraMap_isUnit_inv_apply_eq_iff'] at eq1
+    Module.End_algebraMap_isUnit_inv_apply_eq_iff'] at eq1 
   erw [LocalizedModule.mk_eq, ← IsLocalizedModule.eq_iff_exists S f, f.map_smul, f.map_smul, eq1]
   rfl
 #align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.inj
@@ -1060,12 +1060,12 @@ theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [A
   · intro x
     rw [Module.End_isUnit_iff]
     constructor
-    · rintro a b (e : x • a = x • b); simp_rw [Submonoid.smul_def, Algebra.smul_def] at e
+    · rintro a b (e : x • a = x • b); simp_rw [Submonoid.smul_def, Algebra.smul_def] at e 
       exact (h₁ x x.2).mul_left_cancel e
     · intro a; refine' ⟨((h₁ x x.2).Unit⁻¹ : _) * a, _⟩; change (x : R) • (_ * a) = _
       rw [Algebra.smul_def, ← mul_assoc, IsUnit.mul_val_inv, one_mul]
   · exact h₂
-  · intros ; dsimp; rw [eq_comm, ← sub_eq_zero, ← map_sub, h₃]; simp_rw [smul_sub, sub_eq_zero]
+  · intros; dsimp; rw [eq_comm, ← sub_eq_zero, ← map_sub, h₃]; simp_rw [smul_sub, sub_eq_zero]
 #align is_localized_module.mk_of_algebra IsLocalizedModule.mkOfAlgebra
 
 end Algebra

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

@@ -52,24 +52,12 @@ variable {R : Type u} [CommSemiring R] (S : Submonoid R)
 
 variable (M : Type v) [AddCommMonoid M] [Module R M]
 
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-Case conversion may be inaccurate. Consider using '#align localized_module.r LocalizedModule.rₓ'. -/
 /-- The equivalence relation on `M × S` where `(m1, s1) ≈ (m2, s2)` if and only if
 for some (u : S), u * (s2 • m1 - s1 • m2) = 0-/
 def r (a b : M × S) : Prop :=
   ∃ u : S, u • b.2 • a.1 = u • a.2 • b.1
 #align localized_module.r LocalizedModule.r
 
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 theorem r.isEquiv : IsEquiv _ (r S M) :=
   { refl := fun ⟨m, s⟩ => ⟨1, by rw [one_smul]⟩
     trans := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨m3, s3⟩ ⟨u1, hu1⟩ ⟨u2, hu2⟩ =>
@@ -83,12 +71,6 @@ theorem r.isEquiv : IsEquiv _ (r S M) :=
     symm := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => ⟨u, hu.symm⟩ }
 #align localized_module.r.is_equiv LocalizedModule.r.isEquiv
 
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 instance r.setoid : Setoid (M × S) where
   R := r S M
   iseqv := ⟨(r.isEquiv S M).refl, (r.isEquiv S M).symm, (r.isEquiv S M).trans⟩
@@ -113,50 +95,26 @@ section
 
 variable {M S}
 
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 /-- The canonical map sending `(m, s) ↦ m/s`-/
 def mk (m : M) (s : S) : LocalizedModule S M :=
   Quotient.mk' ⟨m, s⟩
 #align localized_module.mk LocalizedModule.mk
 
-/- warning: localized_module.mk_eq -> LocalizedModule.mk_eq is a dubious translation:
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 theorem mk_eq {m m' : M} {s s' : S} : mk m s = mk m' s' ↔ ∃ u : S, u • s' • m = u • s • m' :=
   Quotient.eq'
 #align localized_module.mk_eq LocalizedModule.mk_eq
 
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 @[elab_as_elim]
 theorem induction_on {β : LocalizedModule S M → Prop} (h : ∀ (m : M) (s : S), β (mk m s)) :
     ∀ x : LocalizedModule S M, β x := by rintro ⟨⟨m, s⟩⟩; exact h m s
 #align localized_module.induction_on LocalizedModule.induction_on
 
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 @[elab_as_elim]
 theorem induction_on₂ {β : LocalizedModule S M → LocalizedModule S M → Prop}
     (h : ∀ (m m' : M) (s s' : S), β (mk m s) (mk m' s')) : ∀ x y, β x y := by
   rintro ⟨⟨m, s⟩⟩ ⟨⟨m', s'⟩⟩; exact h m m' s s'
 #align localized_module.induction_on₂ LocalizedModule.induction_on₂
 
-/- warning: localized_module.lift_on -> LocalizedModule.liftOn is a dubious translation:
-<too large>
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 /-- If `f : M × S → α` respects the equivalence relation `localized_module.r`, then
 `f` descents to a map `localized_module M S → α`.
 -/
@@ -165,16 +123,10 @@ def liftOn {α : Type _} (x : LocalizedModule S M) (f : M × S → α)
   Quotient.liftOn x f wd
 #align localized_module.lift_on LocalizedModule.liftOn
 
-/- warning: localized_module.lift_on_mk -> LocalizedModule.liftOn_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.lift_on_mk LocalizedModule.liftOn_mkₓ'. -/
 theorem liftOn_mk {α : Type _} {f : M × S → α} (wd : ∀ (p p' : M × S) (h1 : p ≈ p'), f p = f p')
     (m : M) (s : S) : liftOn (mk m s) f wd = f ⟨m, s⟩ := by convert Quotient.liftOn_mk f wd ⟨m, s⟩
 #align localized_module.lift_on_mk LocalizedModule.liftOn_mk
 
-/- warning: localized_module.lift_on₂ -> LocalizedModule.liftOn₂ is a dubious translation:
-<too large>
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 /-- If `f : M × S → M × S → α` respects the equivalence relation `localized_module.r`, then
 `f` descents to a map `localized_module M S → localized_module M S → α`.
 -/
@@ -183,9 +135,6 @@ def liftOn₂ {α : Type _} (x y : LocalizedModule S M) (f : M × S → M × S 
   Quotient.liftOn₂ x y f wd
 #align localized_module.lift_on₂ LocalizedModule.liftOn₂
 
-/- warning: localized_module.lift_on₂_mk -> LocalizedModule.liftOn₂_mk is a dubious translation:
-<too large>
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 theorem liftOn₂_mk {α : Type _} (f : M × S → M × S → α)
     (wd : ∀ (p q p' q' : M × S) (h1 : p ≈ p') (h2 : q ≈ q'), f p q = f p' q') (m m' : M)
     (s s' : S) : liftOn₂ (mk m s) (mk m' s') f wd = f ⟨m, s⟩ ⟨m', s'⟩ := by
@@ -195,12 +144,6 @@ theorem liftOn₂_mk {α : Type _} (f : M × S → M × S → α)
 instance : Zero (LocalizedModule S M) :=
   ⟨mk 0 1⟩
 
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-Case conversion may be inaccurate. Consider using '#align localized_module.zero_mk LocalizedModule.zero_mkₓ'. -/
 @[simp]
 theorem zero_mk (s : S) : mk (0 : M) s = 0 :=
   mk_eq.mpr ⟨1, by rw [one_smul, smul_zero, smul_zero, one_smul]⟩
@@ -220,9 +163,6 @@ instance : Add (LocalizedModule S M)
             hu1' hu2'⊢
           rw [hu1', hu2']⟩
 
-/- warning: localized_module.mk_add_mk -> LocalizedModule.mk_add_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.mk_add_mk LocalizedModule.mk_add_mkₓ'. -/
 theorem mk_add_mk {m1 m2 : M} {s1 s2 : S} :
     mk m1 s1 + mk m2 s2 = mk (s2 • m1 + s1 • m2) (s1 * s2) :=
   mk_eq.mpr <| ⟨1, by dsimp only <;> rw [one_smul]⟩
@@ -299,12 +239,6 @@ instance {M : Type _} [AddCommGroup M] [Module R M] : AddCommGroup (LocalizedMod
       rw [lift_on_mk, mk_add_mk]
       simp }
 
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 theorem mk_neg {M : Type _} [AddCommGroup M] [Module R M] {m : M} {s : S} : mk (-m) s = -mk m s :=
   rfl
 #align localized_module.mk_neg LocalizedModule.mk_neg
@@ -392,9 +326,6 @@ instance {A : Type _} [CommRing A] [Algebra R A] {S : Submonoid R} :
       obtain ⟨⟨a₂, s₂⟩, rfl : mk a₂ s₂ = x₂⟩ := Quotient.exists_rep x₂
       exact mk_eq.mpr ⟨1, by simp only [one_smul, mul_comm]⟩ }
 
-/- warning: localized_module.mk_mul_mk -> LocalizedModule.mk_mul_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.mk_mul_mk LocalizedModule.mk_mul_mkₓ'. -/
 theorem mk_mul_mk {A : Type _} [Semiring A] [Algebra R A] {a₁ a₂ : A} {s₁ s₂ : S} :
     mk a₁ s₁ * mk a₂ s₂ = mk (a₁ * a₂) (s₁ * s₂) :=
   rfl
@@ -423,9 +354,6 @@ instance : SMul (Localization S) (LocalizedModule S M)
         ring_nf  at eq1'⊢
         rw [eq1'])
 
-/- warning: localized_module.mk_smul_mk -> LocalizedModule.mk_smul_mk is a dubious translation:
-<too large>
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 theorem mk_smul_mk (r : R) (m : M) (s t : S) : Localization.mk r s • mk m t = mk (r • m) (s * t) :=
   by
   unfold SMul.smul
@@ -484,12 +412,6 @@ private theorem zero_smul' (x : LocalizedModule S M) : (0 : Localization S) •
   induction' x using LocalizedModule.induction_on with m s
   rw [← Localization.mk_zero s, mk_smul_mk, zero_smul, zero_mk]
 
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 instance isModule : Module (Localization S) (LocalizedModule S M)
     where
   smul := (· • ·)
@@ -501,46 +423,25 @@ instance isModule : Module (Localization S) (LocalizedModule S M)
   zero_smul := zero_smul'
 #align localized_module.is_module LocalizedModule.isModule
 
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 @[simp]
 theorem mk_cancel_common_left (s' s : S) (m : M) : mk (s' • m) (s' * s) = mk m s :=
   mk_eq.mpr ⟨1, by simp only [mul_smul, one_smul]; rw [smul_comm]⟩
 #align localized_module.mk_cancel_common_left LocalizedModule.mk_cancel_common_left
 
-/- warning: localized_module.mk_cancel -> LocalizedModule.mk_cancel is a dubious translation:
-<too large>
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 @[simp]
 theorem mk_cancel (s : S) (m : M) : mk (s • m) s = mk m 1 :=
   mk_eq.mpr ⟨1, by simp⟩
 #align localized_module.mk_cancel LocalizedModule.mk_cancel
 
-/- warning: localized_module.mk_cancel_common_right -> LocalizedModule.mk_cancel_common_right is a dubious translation:
-<too large>
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 @[simp]
 theorem mk_cancel_common_right (s s' : S) (m : M) : mk (s' • m) (s * s') = mk m s :=
   mk_eq.mpr ⟨1, by simp [mul_smul]⟩
 #align localized_module.mk_cancel_common_right LocalizedModule.mk_cancel_common_right
 
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 instance isModule' : Module R (LocalizedModule S M) :=
   { Module.compHom (LocalizedModule S M) <| algebraMap R (Localization S) with }
 #align localized_module.is_module' LocalizedModule.isModule'
 
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 theorem smul'_mk (r : R) (s : S) (m : M) : r • mk m s = mk (r • m) s := by
   erw [mk_smul_mk r m 1 s, one_mul]
 #align localized_module.smul'_mk LocalizedModule.smul'_mk
@@ -562,9 +463,6 @@ instance {A : Type _} [Semiring A] [Algebra R A] : Algebra (Localization S) (Loc
       rw [mk_mul_mk, ← Localization.mk_eq_mk', mk_smul_mk, mk_smul_mk, mk_mul_mk, mul_left_comm,
         mul_smul_comm])
 
-/- warning: localized_module.algebra_map_mk -> LocalizedModule.algebraMap_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.algebra_map_mk LocalizedModule.algebraMap_mkₓ'. -/
 theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
     algebraMap _ _ (Localization.mk a s) = mk (algebraMap R A a) s :=
   by
@@ -576,12 +474,6 @@ theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
 instance : IsScalarTower R (Localization S) (LocalizedModule S M) :=
   RestrictScalars.isScalarTower R (Localization S) (LocalizedModule S M)
 
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 instance algebra' {A : Type _} [Semiring A] [Algebra R A] : Algebra R (LocalizedModule S A) :=
   { (algebraMap (Localization S) (LocalizedModule S A)).comp (algebraMap R <| Localization S),
     show Module R (LocalizedModule S A) by
@@ -604,12 +496,6 @@ section
 
 variable (S M)
 
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 /-- The function `m ↦ m / 1` as an `R`-linear map.
 -/
 @[simps]
@@ -622,12 +508,6 @@ def mkLinearMap : M →ₗ[R] LocalizedModule S M
 
 end
 
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 /-- For any `s : S`, there is an `R`-linear map given by `a/b ↦ a/(b*s)`.
 -/
 @[simps]
@@ -647,9 +527,6 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M
   map_smul' r x := x.inductionOn <| by intros ; simp [LocalizedModule.liftOn_mk, smul'_mk]
 #align localized_module.div_by LocalizedModule.divBy
 
-/- warning: localized_module.div_by_mul_by -> LocalizedModule.divBy_mul_by is a dubious translation:
-<too large>
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 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
     divBy s (algebraMap R (Module.End R (LocalizedModule S M)) s p) = p :=
   p.inductionOn
@@ -659,9 +536,6 @@ theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
       erw [mk_cancel_common_left s t])
 #align localized_module.div_by_mul_by LocalizedModule.divBy_mul_by
 
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-<too large>
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 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
     algebraMap R (Module.End R (LocalizedModule S M)) s (divBy s p) = p :=
   p.inductionOn
@@ -702,9 +576,6 @@ class IsLocalizedModule : Prop where
 
 namespace LocalizedModule
 
-/- warning: localized_module.lift' -> LocalizedModule.lift' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.lift' LocalizedModule.lift'ₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 there is a linear map `localized_module S M → M''`.
@@ -734,17 +605,11 @@ noncomputable def lift' (g : M →ₗ[R] M'')
     rfl
 #align localized_module.lift' LocalizedModule.lift'
 
-/- warning: localized_module.lift'_mk -> LocalizedModule.lift'_mk is a dubious translation:
-<too large>
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 theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (m : M) (s : S) : LocalizedModule.lift' S g h (LocalizedModule.mk m s) = (h s).Unit⁻¹.1 (g m) :=
   rfl
 #align localized_module.lift'_mk LocalizedModule.lift'_mk
 
-/- warning: localized_module.lift'_add -> LocalizedModule.lift'_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.lift'_add LocalizedModule.lift'_addₓ'. -/
 theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (x y) :
     LocalizedModule.lift' S g h (x + y) =
@@ -762,9 +627,6 @@ theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
     x y
 #align localized_module.lift'_add LocalizedModule.lift'_add
 
-/- warning: localized_module.lift'_smul -> LocalizedModule.lift'_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.lift'_smul LocalizedModule.lift'_smulₓ'. -/
 theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (r : R) (m) : r • LocalizedModule.lift' S g h m = LocalizedModule.lift' S g h (r • m) :=
   m.inductionOn
@@ -775,9 +637,6 @@ theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (
       erw [← h1.unit⁻¹.1.map_smul, ← g.map_smul])
 #align localized_module.lift'_smul LocalizedModule.lift'_smul
 
-/- warning: localized_module.lift -> LocalizedModule.lift is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.lift LocalizedModule.liftₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 there is a linear map `localized_module S M → M''`.
@@ -790,9 +649,6 @@ noncomputable def lift (g : M →ₗ[R] M'')
   map_smul' r x := by rw [LocalizedModule.lift'_smul, RingHom.id_apply]
 #align localized_module.lift LocalizedModule.lift
 
-/- warning: localized_module.lift_mk -> LocalizedModule.lift_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.lift_mk LocalizedModule.lift_mkₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 `lift g m s = s⁻¹ • g m`.
@@ -802,9 +658,6 @@ theorem lift_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Mod
   rfl
 #align localized_module.lift_mk LocalizedModule.lift_mk
 
-/- warning: localized_module.lift_comp -> LocalizedModule.lift_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.lift_comp LocalizedModule.lift_compₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 there is a linear map `lift g ∘ mk_linear_map = g`.
@@ -816,9 +669,6 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
   erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, one_smul]
 #align localized_module.lift_comp LocalizedModule.lift_comp
 
-/- warning: localized_module.lift_unique -> LocalizedModule.lift_unique is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localized_module.lift_unique LocalizedModule.lift_uniqueₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible and
 `l` is another linear map `localized_module S M ⟶ M''` such that `l ∘ mk_linear_map = g` then
@@ -837,12 +687,6 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
 
 end LocalizedModule
 
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-Case conversion may be inaccurate. Consider using '#align localized_module_is_localized_module localizedModuleIsLocalizedModuleₓ'. -/
 instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule.mkLinearMap S M)
     where
   map_units s :=
@@ -883,9 +727,6 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
 #align is_localized_module.from_localized_module' IsLocalizedModule.fromLocalizedModule'
 -/
 
-/- warning: is_localized_module.from_localized_module'_mk -> IsLocalizedModule.fromLocalizedModule'_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_mk IsLocalizedModule.fromLocalizedModule'_mkₓ'. -/
 @[simp]
 theorem fromLocalizedModule'_mk (m : M) (s : S) :
     fromLocalizedModule' S f (LocalizedModule.mk m s) =
@@ -893,12 +734,6 @@ theorem fromLocalizedModule'_mk (m : M) (s : S) :
   rfl
 #align is_localized_module.from_localized_module'_mk IsLocalizedModule.fromLocalizedModule'_mk
 
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-Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_add IsLocalizedModule.fromLocalizedModule'_addₓ'. -/
 theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
     fromLocalizedModule' S f (x + y) = fromLocalizedModule' S f x + fromLocalizedModule' S f y :=
   LocalizedModule.induction_on₂
@@ -915,9 +750,6 @@ theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
     x y
 #align is_localized_module.from_localized_module'_add IsLocalizedModule.fromLocalizedModule'_add
 
-/- warning: is_localized_module.from_localized_module'_smul -> IsLocalizedModule.fromLocalizedModule'_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_smul IsLocalizedModule.fromLocalizedModule'_smulₓ'. -/
 theorem fromLocalizedModule'_smul (r : R) (x : LocalizedModule S M) :
     r • fromLocalizedModule' S f x = fromLocalizedModule' S f (r • x) :=
   LocalizedModule.induction_on
@@ -928,12 +760,6 @@ theorem fromLocalizedModule'_smul (r : R) (x : LocalizedModule S M) :
     x
 #align is_localized_module.from_localized_module'_smul IsLocalizedModule.fromLocalizedModule'_smul
 
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-Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module IsLocalizedModule.fromLocalizedModuleₓ'. -/
 /-- If `(M', f : M ⟶ M')` satisfies universal property of localized module, there is a canonical map
 `localized_module S M ⟶ M'`.
 -/
@@ -944,21 +770,12 @@ noncomputable def fromLocalizedModule : LocalizedModule S M →ₗ[R] M'
   map_smul' r x := by rw [from_localized_module'_smul, RingHom.id_apply]
 #align is_localized_module.from_localized_module IsLocalizedModule.fromLocalizedModule
 
-/- warning: is_localized_module.from_localized_module_mk -> IsLocalizedModule.fromLocalizedModule_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module_mk IsLocalizedModule.fromLocalizedModule_mkₓ'. -/
 theorem fromLocalizedModule_mk (m : M) (s : S) :
     fromLocalizedModule S f (LocalizedModule.mk m s) =
       (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
   rfl
 #align is_localized_module.from_localized_module_mk IsLocalizedModule.fromLocalizedModule_mk
 
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 theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f := fun x y eq1 =>
   by
   induction' x using LocalizedModule.induction_on with a b
@@ -971,34 +788,16 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
   rfl
 #align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.inj
 
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 theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S f := fun x =>
   let ⟨⟨m, s⟩, eq1⟩ := IsLocalizedModule.surj S f x
   ⟨LocalizedModule.mk m s, by
     rw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← eq1]; rfl⟩
 #align is_localized_module.from_localized_module.surj IsLocalizedModule.fromLocalizedModule.surj
 
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 theorem fromLocalizedModule.bij : Function.Bijective <| fromLocalizedModule S f :=
   ⟨fromLocalizedModule.inj _ _, fromLocalizedModule.surj _ _⟩
 #align is_localized_module.from_localized_module.bij IsLocalizedModule.fromLocalizedModule.bij
 
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 /--
 If `(M', f : M ⟶ M')` satisfies universal property of localized module, then `M'` is isomorphic to
 `localized_module S M` as an `R`-module.
@@ -1009,17 +808,11 @@ noncomputable def iso : LocalizedModule S M ≃ₗ[R] M' :=
     Equiv.ofBijective (fromLocalizedModule S f) <| fromLocalizedModule.bij _ _ with }
 #align is_localized_module.iso IsLocalizedModule.iso
 
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-<too large>
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 theorem iso_apply_mk (m : M) (s : S) :
     iso S f (LocalizedModule.mk m s) = (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
   rfl
 #align is_localized_module.iso_apply_mk IsLocalizedModule.iso_apply_mk
 
-/- warning: is_localized_module.iso_symm_apply_aux -> IsLocalizedModule.iso_symm_apply_aux is a dubious translation:
-<too large>
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 theorem iso_symm_apply_aux (m : M') :
     (iso S f).symm m =
       LocalizedModule.mk (IsLocalizedModule.surj S f m).some.1
@@ -1032,9 +825,6 @@ theorem iso_symm_apply_aux (m : M') :
   erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff', h2.some_spec]
 #align is_localized_module.iso_symm_apply_aux IsLocalizedModule.iso_symm_apply_aux
 
-/- warning: is_localized_module.iso_symm_apply' -> IsLocalizedModule.iso_symm_apply' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'ₓ'. -/
 theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
     (iso S f).symm m = LocalizedModule.mk a b :=
   (iso_symm_apply_aux S f m).trans <|
@@ -1044,18 +834,12 @@ theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
         mul_smul, mul_comm, mul_smul, eq1]
 #align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'
 
-/- warning: is_localized_module.iso_symm_comp -> IsLocalizedModule.iso_symm_comp is a dubious translation:
-<too large>
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 theorem iso_symm_comp : (iso S f).symm.toLinearMap.comp f = LocalizedModule.mkLinearMap S M :=
   by
   ext m; rw [LinearMap.comp_apply, LocalizedModule.mkLinearMap_apply]
   change (iso S f).symm _ = _; rw [iso_symm_apply']; exact one_smul _ _
 #align is_localized_module.iso_symm_comp IsLocalizedModule.iso_symm_comp
 
-/- warning: is_localized_module.lift -> IsLocalizedModule.lift is a dubious translation:
-<too large>
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 /--
 If `M'` is a localized module and `g` is a linear map `M' → M''` such that all scalar multiplication
 by `s : S` is invertible, then there is a linear map `M' → M''`.
@@ -1065,9 +849,6 @@ noncomputable def lift (g : M →ₗ[R] M'')
   (LocalizedModule.lift S g h).comp (iso S f).symm.toLinearMap
 #align is_localized_module.lift IsLocalizedModule.lift
 
-/- warning: is_localized_module.lift_comp -> IsLocalizedModule.lift_comp is a dubious translation:
-<too large>
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 theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x)) :
     (lift S f g h).comp f = g :=
   by
@@ -1077,9 +858,6 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
   exact iso_symm_comp _ _
 #align is_localized_module.lift_comp IsLocalizedModule.lift_comp
 
-/- warning: is_localized_module.lift_unique -> IsLocalizedModule.lift_unique is a dubious translation:
-<too large>
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 theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (l : M' →ₗ[R] M'') (hl : l.comp f = g) : lift S f g h = l :=
   by
@@ -1092,9 +870,6 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
     erw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, one_smul]
 #align is_localized_module.lift_unique IsLocalizedModule.lift_unique
 
-/- warning: is_localized_module.is_universal -> IsLocalizedModule.is_universal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localized_module.is_universal IsLocalizedModule.is_universalₓ'. -/
 /-- Universal property from localized module:
 If `(M', f : M ⟶ M')` is a localized module then it satisfies the following universal property:
 For every `R`-module `M''` which every `s : S`-scalar multiplication is invertible and for every
@@ -1115,9 +890,6 @@ theorem is_universal :
   fun g h => ⟨lift S f g h, lift_comp S f g h, fun l hl => (lift_unique S f g h l hl).symm⟩
 #align is_localized_module.is_universal IsLocalizedModule.is_universal
 
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-<too large>
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 theorem ringHom_ext (map_unit : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     ⦃j k : M' →ₗ[R] M''⦄ (h : j.comp f = k.comp f) : j = k := by
   rw [← lift_unique S f (k.comp f) map_unit j h, lift_unique]; rfl
@@ -1134,61 +906,34 @@ noncomputable def linearEquiv [IsLocalizedModule S g] : M' ≃ₗ[R] M'' :=
 
 variable {S}
 
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 theorem smul_injective (s : S) : Function.Injective fun m : M' => s • m :=
   ((Module.End_isUnit_iff _).mp (IsLocalizedModule.map_units f s)).Injective
 #align is_localized_module.smul_injective IsLocalizedModule.smul_injective
 
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 theorem smul_inj (s : S) (m₁ m₂ : M') : s • m₁ = s • m₂ ↔ m₁ = m₂ :=
   (smul_injective f s).eq_iff
 #align is_localized_module.smul_inj IsLocalizedModule.smul_inj
 
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 /-- `mk' f m s` is the fraction `m/s` with respect to the localization map `f`. -/
 noncomputable def mk' (m : M) (s : S) : M' :=
   fromLocalizedModule S f (LocalizedModule.mk m s)
 #align is_localized_module.mk' IsLocalizedModule.mk'
 
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 theorem mk'_smul (r : R) (m : M) (s : S) : mk' f (r • m) s = r • mk' f m s := by delta mk';
   rw [← LocalizedModule.smul'_mk, LinearMap.map_smul]
 #align is_localized_module.mk'_smul IsLocalizedModule.mk'_smul
 
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 theorem mk'_add_mk' (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ + mk' f m₂ s₂ = mk' f (s₂ • m₁ + s₁ • m₂) (s₁ * s₂) := by delta mk';
   rw [← map_add, LocalizedModule.mk_add_mk]
 #align is_localized_module.mk'_add_mk' IsLocalizedModule.mk'_add_mk'
 
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 @[simp]
 theorem mk'_zero (s : S) : mk' f 0 s = 0 := by rw [← zero_smul R (0 : M), mk'_smul, zero_smul]
 #align is_localized_module.mk'_zero IsLocalizedModule.mk'_zero
 
 variable (S)
 
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 @[simp]
 theorem mk'_one (m : M) : mk' f m (1 : S) = f m := by delta mk';
   rw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, Submonoid.coe_one,
@@ -1197,51 +942,30 @@ theorem mk'_one (m : M) : mk' f m (1 : S) = f m := by delta mk';
 
 variable {S}
 
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 @[simp]
 theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m := by delta mk';
   rw [LocalizedModule.mk_cancel, ← mk'_one S f]; rfl
 #align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancel
 
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 @[simp]
 theorem mk'_cancel' (m : M) (s : S) : s • mk' f m s = f m := by
   rw [Submonoid.smul_def, ← mk'_smul, ← Submonoid.smul_def, mk'_cancel]
 #align is_localized_module.mk'_cancel' IsLocalizedModule.mk'_cancel'
 
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 @[simp]
 theorem mk'_cancel_left (m : M) (s₁ s₂ : S) : mk' f (s₁ • m) (s₁ * s₂) = mk' f m s₂ := by delta mk';
   rw [LocalizedModule.mk_cancel_common_left]
 #align is_localized_module.mk'_cancel_left IsLocalizedModule.mk'_cancel_left
 
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 @[simp]
 theorem mk'_cancel_right (m : M) (s₁ s₂ : S) : mk' f (s₂ • m) (s₁ * s₂) = mk' f m s₁ := by
   delta mk'; rw [LocalizedModule.mk_cancel_common_right]
 #align is_localized_module.mk'_cancel_right IsLocalizedModule.mk'_cancel_right
 
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 theorem mk'_add (m₁ m₂ : M) (s : S) : mk' f (m₁ + m₂) s = mk' f m₁ s + mk' f m₂ s := by
   rw [mk'_add_mk', ← smul_add, mk'_cancel_left]
 #align is_localized_module.mk'_add IsLocalizedModule.mk'_add
 
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 theorem mk'_eq_mk'_iff (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ = mk' f m₂ s₂ ↔ ∃ s : S, s • s₁ • m₂ = s • s₂ • m₁ :=
   by
@@ -1250,41 +974,23 @@ theorem mk'_eq_mk'_iff (m₁ m₂ : M) (s₁ s₂ : S) :
   simp_rw [eq_comm]
 #align is_localized_module.mk'_eq_mk'_iff IsLocalizedModule.mk'_eq_mk'_iff
 
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 theorem mk'_neg {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m : M) (s : S) : mk' f (-m) s = -mk' f m s := by
   delta mk'; rw [LocalizedModule.mk_neg, map_neg]
 #align is_localized_module.mk'_neg IsLocalizedModule.mk'_neg
 
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 theorem mk'_sub {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m₁ m₂ : M) (s : S) :
     mk' f (m₁ - m₂) s = mk' f m₁ s - mk' f m₂ s := by
   rw [sub_eq_add_neg, sub_eq_add_neg, mk'_add, mk'_neg]
 #align is_localized_module.mk'_sub IsLocalizedModule.mk'_sub
 
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 theorem mk'_sub_mk' {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ - mk' f m₂ s₂ = mk' f (s₂ • m₁ - s₁ • m₂) (s₁ * s₂) := by
   rw [sub_eq_add_neg, ← mk'_neg, mk'_add_mk', smul_neg, ← sub_eq_add_neg]
 #align is_localized_module.mk'_sub_mk' IsLocalizedModule.mk'_sub_mk'
 
-/- warning: is_localized_module.mk'_mul_mk'_of_map_mul -> IsLocalizedModule.mk'_mul_mk'_of_map_mul is a dubious translation:
-<too large>
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 theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Module R M]
     [Algebra R M'] (f : M →ₗ[R] M') (hf : ∀ m₁ m₂, f (m₁ * m₂) = f m₁ * f m₂)
     [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
@@ -1297,9 +1003,6 @@ theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Modul
   simp_rw [← Submonoid.smul_def, mk'_cancel, smul_eq_mul, hf]
 #align is_localized_module.mk'_mul_mk'_of_map_mul IsLocalizedModule.mk'_mul_mk'_of_map_mul
 
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 theorem mk'_mul_mk' {M M' : Type _} [Semiring M] [Semiring M'] [Algebra R M] [Algebra R M']
     (f : M →ₐ[R] M') [IsLocalizedModule S f.toLinearMap] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f.toLinearMap m₁ s₁ * mk' f.toLinearMap m₂ s₂ = mk' f.toLinearMap (m₁ * m₂) (s₁ * s₂) :=
@@ -1308,36 +1011,21 @@ theorem mk'_mul_mk' {M M' : Type _} [Semiring M] [Semiring M'] [Algebra R M] [Al
 
 variable {f}
 
-/- warning: is_localized_module.mk'_eq_iff -> IsLocalizedModule.mk'_eq_iff is a dubious translation:
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 @[simp]
 theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m' := by
   rw [← smul_inj f s, Submonoid.smul_def, ← mk'_smul, ← Submonoid.smul_def, mk'_cancel]
 #align is_localized_module.mk'_eq_iff IsLocalizedModule.mk'_eq_iff
 
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 @[simp]
 theorem mk'_eq_zero {m : M} (s : S) : mk' f m s = 0 ↔ f m = 0 := by rw [mk'_eq_iff, smul_zero]
 #align is_localized_module.mk'_eq_zero IsLocalizedModule.mk'_eq_zero
 
 variable (f)
 
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 theorem mk'_eq_zero' {m : M} (s : S) : mk' f m s = 0 ↔ ∃ s' : S, s' • m = 0 := by
   simp_rw [← mk'_zero f (1 : S), mk'_eq_mk'_iff, smul_zero, one_smul, eq_comm]
 #align is_localized_module.mk'_eq_zero' IsLocalizedModule.mk'_eq_zero'
 
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-Case conversion may be inaccurate. Consider using '#align is_localized_module.mk_eq_mk' IsLocalizedModule.mk_eq_mk'ₓ'. -/
 theorem mk_eq_mk' (s : S) (m : M) :
     LocalizedModule.mk m s = mk' (LocalizedModule.mkLinearMap S M) m s := by
   rw [eq_comm, mk'_eq_iff, Submonoid.smul_def, LocalizedModule.smul'_mk, ← Submonoid.smul_def,
@@ -1346,19 +1034,10 @@ theorem mk_eq_mk' (s : S) (m : M) :
 
 variable (S)
 
-/- warning: is_localized_module.eq_zero_iff -> IsLocalizedModule.eq_zero_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localized_module.eq_zero_iff IsLocalizedModule.eq_zero_iffₓ'. -/
 theorem eq_zero_iff {m : M} : f m = 0 ↔ ∃ s' : S, s' • m = 0 :=
   (mk'_eq_zero (1 : S)).symm.trans (mk'_eq_zero' f _)
 #align is_localized_module.eq_zero_iff IsLocalizedModule.eq_zero_iff
 
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 theorem mk'_surjective : Function.Surjective (Function.uncurry <| mk' f : M × S → M') :=
   by
   intro x
@@ -1368,9 +1047,6 @@ theorem mk'_surjective : Function.Surjective (Function.uncurry <| mk' f : M × S
 
 section Algebra
 
-/- warning: is_localized_module.mk_of_algebra -> IsLocalizedModule.mkOfAlgebra is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localized_module.mk_of_algebra IsLocalizedModule.mkOfAlgebraₓ'. -/
 theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [Algebra R S]
     [Algebra R S'] (M : Submonoid R) (f : S →ₐ[R] S') (h₁ : ∀ x ∈ M, IsUnit (algebraMap R S' x))
     (h₂ : ∀ y, ∃ x : S × M, x.2 • y = f x.1) (h₃ : ∀ x, f x = 0 → ∃ m : M, m • x = 0) :

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

@@ -139,9 +139,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align localized_module.induction_on LocalizedModule.induction_onₓ'. -/
 @[elab_as_elim]
 theorem induction_on {β : LocalizedModule S M → Prop} (h : ∀ (m : M) (s : S), β (mk m s)) :
-    ∀ x : LocalizedModule S M, β x := by
-  rintro ⟨⟨m, s⟩⟩
-  exact h m s
+    ∀ x : LocalizedModule S M, β x := by rintro ⟨⟨m, s⟩⟩; exact h m s
 #align localized_module.induction_on LocalizedModule.induction_on
 
 /- warning: localized_module.induction_on₂ -> LocalizedModule.induction_on₂ is a dubious translation:
@@ -152,10 +150,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align localized_module.induction_on₂ LocalizedModule.induction_on₂ₓ'. -/
 @[elab_as_elim]
 theorem induction_on₂ {β : LocalizedModule S M → LocalizedModule S M → Prop}
-    (h : ∀ (m m' : M) (s s' : S), β (mk m s) (mk m' s')) : ∀ x y, β x y :=
-  by
-  rintro ⟨⟨m, s⟩⟩ ⟨⟨m', s'⟩⟩
-  exact h m m' s s'
+    (h : ∀ (m m' : M) (s s' : S), β (mk m s) (mk m' s')) : ∀ x y, β x y := by
+  rintro ⟨⟨m, s⟩⟩ ⟨⟨m', s'⟩⟩; exact h m m' s s'
 #align localized_module.induction_on₂ LocalizedModule.induction_on₂
 
 /- warning: localized_module.lift_on -> LocalizedModule.liftOn is a dubious translation:
@@ -290,17 +286,13 @@ instance {M : Type _} [AddCommGroup M] [Module R M] : AddCommGroup (LocalizedMod
     show AddCommMonoid (LocalizedModule S M) by
       infer_instance with
     neg := fun p =>
-      liftOn p (fun x => LocalizedModule.mk (-x.1) x.2) fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ =>
-        by
-        rw [mk_eq]
-        exact ⟨u, by simpa⟩
+      liftOn p (fun x => LocalizedModule.mk (-x.1) x.2) fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => by
+        rw [mk_eq]; exact ⟨u, by simpa⟩
     add_left_neg := fun p =>
       by
       obtain ⟨⟨m, s⟩, rfl : mk m s = p⟩ := Quotient.exists_rep p
       change
-        ((mk m s).liftOn (fun x => mk (-x.1) x.2) fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ =>
-              by
-              rw [mk_eq]
+        ((mk m s).liftOn (fun x => mk (-x.1) x.2) fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => by rw [mk_eq];
               exact ⟨u, by simpa⟩) +
             mk m s =
           0
@@ -514,10 +506,7 @@ instance isModule : Module (Localization S) (LocalizedModule S M)
 Case conversion may be inaccurate. Consider using '#align localized_module.mk_cancel_common_left LocalizedModule.mk_cancel_common_leftₓ'. -/
 @[simp]
 theorem mk_cancel_common_left (s' s : S) (m : M) : mk (s' • m) (s' * s) = mk m s :=
-  mk_eq.mpr
-    ⟨1, by
-      simp only [mul_smul, one_smul]
-      rw [smul_comm]⟩
+  mk_eq.mpr ⟨1, by simp only [mul_smul, one_smul]; rw [smul_comm]⟩
 #align localized_module.mk_cancel_common_left LocalizedModule.mk_cancel_common_left
 
 /- warning: localized_module.mk_cancel -> LocalizedModule.mk_cancel is a dubious translation:
@@ -653,15 +642,9 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M
         intro m₁ m₂ t₁ t₂
         simp only [mk_add_mk, LocalizedModule.liftOn_mk, mul_smul, ← smul_add, mul_assoc,
           mk_cancel_common_left s]
-        rw [show s * (t₁ * t₂) = t₁ * (s * t₂) by
-            ext
-            simp only [Submonoid.coe_mul]
-            ring])
+        rw [show s * (t₁ * t₂) = t₁ * (s * t₂) by ext; simp only [Submonoid.coe_mul]; ring])
       y
-  map_smul' r x :=
-    x.inductionOn <| by
-      intros
-      simp [LocalizedModule.liftOn_mk, smul'_mk]
+  map_smul' r x := x.inductionOn <| by intros ; simp [LocalizedModule.liftOn_mk, smul'_mk]
 #align localized_module.div_by LocalizedModule.divBy
 
 /- warning: localized_module.div_by_mul_by -> LocalizedModule.divBy_mul_by is a dubious translation:
@@ -732,18 +715,13 @@ noncomputable def lift' (g : M →ₗ[R] M'')
   m.liftOn (fun p => (h <| p.2).Unit⁻¹ <| g p.1) fun ⟨m, s⟩ ⟨m', s'⟩ ⟨c, eq1⟩ =>
     by
     generalize_proofs h1 h2
-    erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← h2.unit⁻¹.1.map_smul]
-    symm
-    erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff]
-    dsimp
-    have : c • s • g m' = c • s' • g m :=
-      by
-      erw [← g.map_smul, ← g.map_smul, ← g.map_smul, ← g.map_smul, eq1]
-      rfl
+    erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← h2.unit⁻¹.1.map_smul]; symm
+    erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff]; dsimp
+    have : c • s • g m' = c • s' • g m := by
+      erw [← g.map_smul, ← g.map_smul, ← g.map_smul, ← g.map_smul, eq1]; rfl
     have : Function.Injective (h c).Unit.inv :=
       by
-      rw [Function.injective_iff_hasLeftInverse]
-      refine' ⟨(h c).Unit, _⟩
+      rw [Function.injective_iff_hasLeftInverse]; refine' ⟨(h c).Unit, _⟩
       intro x
       change ((h c).Unit.1 * (h c).Unit.inv) x = x
       simp only [Units.inv_eq_val_inv, IsUnit.mul_val_inv, LinearMap.one_apply]
@@ -871,10 +849,7 @@ instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule
     ⟨⟨algebraMap R (Module.End R (LocalizedModule S M)) s, LocalizedModule.divBy s,
         FunLike.ext _ _ <| LocalizedModule.mul_by_divBy s,
         FunLike.ext _ _ <| LocalizedModule.divBy_mul_by s⟩,
-      FunLike.ext _ _ fun p =>
-        p.inductionOn <| by
-          intros
-          rfl⟩
+      FunLike.ext _ _ fun p => p.inductionOn <| by intros ; rfl⟩
   surj p :=
     p.inductionOn
       (by
@@ -935,12 +910,8 @@ theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
         h3.unit⁻¹.1.map_smul, map_add]
       congr 1
       all_goals erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff']
-      · dsimp
-        erw [mul_smul, f.map_smul]
-        rfl
-      · dsimp
-        erw [mul_comm, f.map_smul, mul_smul]
-        rfl)
+      · dsimp; erw [mul_smul, f.map_smul]; rfl
+      · dsimp; erw [mul_comm, f.map_smul, mul_smul]; rfl)
     x y
 #align is_localized_module.from_localized_module'_add IsLocalizedModule.fromLocalizedModule'_add
 
@@ -1008,10 +979,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.surj IsLocalizedModule.fromLocalizedModule.surjₓ'. -/
 theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S f := fun x =>
   let ⟨⟨m, s⟩, eq1⟩ := IsLocalizedModule.surj S f x
-  ⟨LocalizedModule.mk m s,
-    by
-    rw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← eq1]
-    rfl⟩
+  ⟨LocalizedModule.mk m s, by
+    rw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← eq1]; rfl⟩
 #align is_localized_module.from_localized_module.surj IsLocalizedModule.fromLocalizedModule.surj
 
 /- warning: is_localized_module.from_localized_module.bij -> IsLocalizedModule.fromLocalizedModule.bij is a dubious translation:
@@ -1119,9 +1088,7 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
     show (iso S f).toLinearMap.comp (iso S f).symm.toLinearMap = LinearMap.id from _,
     LinearMap.comp_id]
   · rw [LinearEquiv.comp_toLinearMap_symm_eq, LinearMap.id_comp]
-  · rw [LinearMap.comp_assoc, ← hl]
-    congr 1
-    ext x
+  · rw [LinearMap.comp_assoc, ← hl]; congr 1; ext x
     erw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, one_smul]
 #align is_localized_module.lift_unique IsLocalizedModule.lift_unique
 
@@ -1152,10 +1119,8 @@ theorem is_universal :
 <too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.ring_hom_ext IsLocalizedModule.ringHom_extₓ'. -/
 theorem ringHom_ext (map_unit : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
-    ⦃j k : M' →ₗ[R] M''⦄ (h : j.comp f = k.comp f) : j = k :=
-  by
-  rw [← lift_unique S f (k.comp f) map_unit j h, lift_unique]
-  rfl
+    ⦃j k : M' →ₗ[R] M''⦄ (h : j.comp f = k.comp f) : j = k := by
+  rw [← lift_unique S f (k.comp f) map_unit j h, lift_unique]; rfl
 #align is_localized_module.ring_hom_ext IsLocalizedModule.ringHom_ext
 
 #print IsLocalizedModule.linearEquiv /-
@@ -1197,9 +1162,7 @@ noncomputable def mk' (m : M) (s : S) : M' :=
 /- warning: is_localized_module.mk'_smul -> IsLocalizedModule.mk'_smul is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_smul IsLocalizedModule.mk'_smulₓ'. -/
-theorem mk'_smul (r : R) (m : M) (s : S) : mk' f (r • m) s = r • mk' f m s :=
-  by
-  delta mk'
+theorem mk'_smul (r : R) (m : M) (s : S) : mk' f (r • m) s = r • mk' f m s := by delta mk';
   rw [← LocalizedModule.smul'_mk, LinearMap.map_smul]
 #align is_localized_module.mk'_smul IsLocalizedModule.mk'_smul
 
@@ -1207,9 +1170,7 @@ theorem mk'_smul (r : R) (m : M) (s : S) : mk' f (r • m) s = r • mk' f m s :
 <too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_add_mk' IsLocalizedModule.mk'_add_mk'ₓ'. -/
 theorem mk'_add_mk' (m₁ m₂ : M) (s₁ s₂ : S) :
-    mk' f m₁ s₁ + mk' f m₂ s₂ = mk' f (s₂ • m₁ + s₁ • m₂) (s₁ * s₂) :=
-  by
-  delta mk'
+    mk' f m₁ s₁ + mk' f m₂ s₂ = mk' f (s₂ • m₁ + s₁ • m₂) (s₁ * s₂) := by delta mk';
   rw [← map_add, LocalizedModule.mk_add_mk]
 #align is_localized_module.mk'_add_mk' IsLocalizedModule.mk'_add_mk'
 
@@ -1229,9 +1190,7 @@ variable (S)
 <too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_one IsLocalizedModule.mk'_oneₓ'. -/
 @[simp]
-theorem mk'_one (m : M) : mk' f m (1 : S) = f m :=
-  by
-  delta mk'
+theorem mk'_one (m : M) : mk' f m (1 : S) = f m := by delta mk';
   rw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, Submonoid.coe_one,
     one_smul]
 #align is_localized_module.mk'_one IsLocalizedModule.mk'_one
@@ -1242,11 +1201,8 @@ variable {S}
 <too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancelₓ'. -/
 @[simp]
-theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m :=
-  by
-  delta mk'
-  rw [LocalizedModule.mk_cancel, ← mk'_one S f]
-  rfl
+theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m := by delta mk';
+  rw [LocalizedModule.mk_cancel, ← mk'_one S f]; rfl
 #align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancel
 
 /- warning: is_localized_module.mk'_cancel' -> IsLocalizedModule.mk'_cancel' is a dubious translation:
@@ -1261,9 +1217,7 @@ theorem mk'_cancel' (m : M) (s : S) : s • mk' f m s = f m := by
 <too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel_left IsLocalizedModule.mk'_cancel_leftₓ'. -/
 @[simp]
-theorem mk'_cancel_left (m : M) (s₁ s₂ : S) : mk' f (s₁ • m) (s₁ * s₂) = mk' f m s₂ :=
-  by
-  delta mk'
+theorem mk'_cancel_left (m : M) (s₁ s₂ : S) : mk' f (s₁ • m) (s₁ * s₂) = mk' f m s₂ := by delta mk';
   rw [LocalizedModule.mk_cancel_common_left]
 #align is_localized_module.mk'_cancel_left IsLocalizedModule.mk'_cancel_left
 
@@ -1271,10 +1225,8 @@ theorem mk'_cancel_left (m : M) (s₁ s₂ : S) : mk' f (s₁ • m) (s₁ * s
 <too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel_right IsLocalizedModule.mk'_cancel_rightₓ'. -/
 @[simp]
-theorem mk'_cancel_right (m : M) (s₁ s₂ : S) : mk' f (s₂ • m) (s₁ * s₂) = mk' f m s₁ :=
-  by
-  delta mk'
-  rw [LocalizedModule.mk_cancel_common_right]
+theorem mk'_cancel_right (m : M) (s₁ s₂ : S) : mk' f (s₂ • m) (s₁ * s₂) = mk' f m s₁ := by
+  delta mk'; rw [LocalizedModule.mk_cancel_common_right]
 #align is_localized_module.mk'_cancel_right IsLocalizedModule.mk'_cancel_right
 
 /- warning: is_localized_module.mk'_add -> IsLocalizedModule.mk'_add is a dubious translation:
@@ -1305,10 +1257,8 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {M : Type.{u3}} {M' : Type.{u2}} [_inst_9 : AddCommGroup.{u3} M] [_inst_10 : AddCommGroup.{u2} M'] [_inst_11 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_9)] [_inst_12 : Module.{u1, u2} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_10)] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_9) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_10) _inst_11 _inst_12) [_inst_13 : IsLocalizedModule.{u1, u3, u2} R _inst_1 S M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_9) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_10) _inst_11 _inst_12 f] (m : M) (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_9) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_10) _inst_11 _inst_12 f _inst_13 (Neg.neg.{u3} M (NegZeroClass.toNeg.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_9))))) m) s) (Neg.neg.{u2} M' (NegZeroClass.toNeg.{u2} M' (SubNegZeroMonoid.toNegZeroClass.{u2} M' (SubtractionMonoid.toSubNegZeroMonoid.{u2} M' (SubtractionCommMonoid.toSubtractionMonoid.{u2} M' (AddCommGroup.toDivisionAddCommMonoid.{u2} M' _inst_10))))) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_9) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_10) _inst_11 _inst_12 f _inst_13 m s))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_neg IsLocalizedModule.mk'_negₓ'. -/
 theorem mk'_neg {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
-    (f : M →ₗ[R] M') [IsLocalizedModule S f] (m : M) (s : S) : mk' f (-m) s = -mk' f m s :=
-  by
-  delta mk'
-  rw [LocalizedModule.mk_neg, map_neg]
+    (f : M →ₗ[R] M') [IsLocalizedModule S f] (m : M) (s : S) : mk' f (-m) s = -mk' f m s := by
+  delta mk'; rw [LocalizedModule.mk_neg, map_neg]
 #align is_localized_module.mk'_neg IsLocalizedModule.mk'_neg
 
 /- warning: is_localized_module.mk'_sub -> IsLocalizedModule.mk'_sub is a dubious translation:
@@ -1428,25 +1378,18 @@ theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [A
   by
   replace h₃ := fun x =>
     Iff.intro (h₃ x) fun ⟨⟨m, hm⟩, e⟩ =>
-      (h₁ m hm).mul_left_cancel <| by
-        rw [← Algebra.smul_def]
+      (h₁ m hm).mul_left_cancel <| by rw [← Algebra.smul_def];
         simpa [Submonoid.smul_def] using f.congr_arg e
   constructor
   · intro x
     rw [Module.End_isUnit_iff]
     constructor
-    · rintro a b (e : x • a = x • b)
-      simp_rw [Submonoid.smul_def, Algebra.smul_def] at e
+    · rintro a b (e : x • a = x • b); simp_rw [Submonoid.smul_def, Algebra.smul_def] at e
       exact (h₁ x x.2).mul_left_cancel e
-    · intro a
-      refine' ⟨((h₁ x x.2).Unit⁻¹ : _) * a, _⟩
-      change (x : R) • (_ * a) = _
+    · intro a; refine' ⟨((h₁ x x.2).Unit⁻¹ : _) * a, _⟩; change (x : R) • (_ * a) = _
       rw [Algebra.smul_def, ← mul_assoc, IsUnit.mul_val_inv, one_mul]
   · exact h₂
-  · intros
-    dsimp
-    rw [eq_comm, ← sub_eq_zero, ← map_sub, h₃]
-    simp_rw [smul_sub, sub_eq_zero]
+  · intros ; dsimp; rw [eq_comm, ← sub_eq_zero, ← map_sub, h₃]; simp_rw [smul_sub, sub_eq_zero]
 #align is_localized_module.mk_of_algebra IsLocalizedModule.mkOfAlgebra
 
 end Algebra

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

@@ -125,10 +125,7 @@ def mk (m : M) (s : S) : LocalizedModule S M :=
 #align localized_module.mk LocalizedModule.mk
 
 /- warning: localized_module.mk_eq -> LocalizedModule.mk_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align localized_module.mk_eq LocalizedModule.mk_eqₓ'. -/
 theorem mk_eq {m m' : M} {s s' : S} : mk m s = mk m' s' ↔ ∃ u : S, u • s' • m = u • s • m' :=
   Quotient.eq'
@@ -162,10 +159,7 @@ theorem induction_on₂ {β : LocalizedModule S M → LocalizedModule S M → Pr
 #align localized_module.induction_on₂ LocalizedModule.induction_on₂
 
 /- warning: localized_module.lift_on -> LocalizedModule.liftOn is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align localized_module.lift_on LocalizedModule.liftOnₓ'. -/
 /-- If `f : M × S → α` respects the equivalence relation `localized_module.r`, then
 `f` descents to a map `localized_module M S → α`.
@@ -176,20 +170,14 @@ def liftOn {α : Type _} (x : LocalizedModule S M) (f : M × S → α)
 #align localized_module.lift_on LocalizedModule.liftOn
 
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 Case conversion may be inaccurate. Consider using '#align localized_module.lift_on_mk LocalizedModule.liftOn_mkₓ'. -/
 theorem liftOn_mk {α : Type _} {f : M × S → α} (wd : ∀ (p p' : M × S) (h1 : p ≈ p'), f p = f p')
     (m : M) (s : S) : liftOn (mk m s) f wd = f ⟨m, s⟩ := by convert Quotient.liftOn_mk f wd ⟨m, s⟩
 #align localized_module.lift_on_mk LocalizedModule.liftOn_mk
 
 /- warning: localized_module.lift_on₂ -> LocalizedModule.liftOn₂ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift_on₂ LocalizedModule.liftOn₂ₓ'. -/
 /-- If `f : M × S → M × S → α` respects the equivalence relation `localized_module.r`, then
 `f` descents to a map `localized_module M S → localized_module M S → α`.
@@ -200,10 +188,7 @@ def liftOn₂ {α : Type _} (x y : LocalizedModule S M) (f : M × S → M × S 
 #align localized_module.lift_on₂ LocalizedModule.liftOn₂
 
 /- warning: localized_module.lift_on₂_mk -> LocalizedModule.liftOn₂_mk is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift_on₂_mk LocalizedModule.liftOn₂_mkₓ'. -/
 theorem liftOn₂_mk {α : Type _} (f : M × S → M × S → α)
     (wd : ∀ (p q p' q' : M × S) (h1 : p ≈ p') (h2 : q ≈ q'), f p q = f p' q') (m m' : M)
@@ -240,10 +225,7 @@ instance : Add (LocalizedModule S M)
           rw [hu1', hu2']⟩
 
 /- warning: localized_module.mk_add_mk -> LocalizedModule.mk_add_mk is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align localized_module.mk_add_mk LocalizedModule.mk_add_mkₓ'. -/
 theorem mk_add_mk {m1 m2 : M} {s1 s2 : S} :
     mk m1 s1 + mk m2 s2 = mk (s2 • m1 + s1 • m2) (s1 * s2) :=
@@ -261,12 +243,10 @@ private theorem add_assoc' (x y z : LocalizedModule S M) : x + y + z = x + (y +
   congr 1
   · rw [mul_assoc]
   · rw [eq_comm, mul_comm, add_assoc, mul_smul, mul_smul, ← mul_smul sx sz, mul_comm, mul_smul]
-#align localized_module.add_assoc' localized_module.add_assoc'
 
 private theorem add_comm' (x y : LocalizedModule S M) : x + y = y + x :=
   LocalizedModule.induction_on₂ (fun m m' s s' => by rw [mk_add_mk, mk_add_mk, add_comm, mul_comm])
     x y
-#align localized_module.add_comm' localized_module.add_comm'
 
 private theorem zero_add' (x : LocalizedModule S M) : 0 + x = x :=
   induction_on
@@ -274,7 +254,6 @@ private theorem zero_add' (x : LocalizedModule S M) : 0 + x = x :=
       rw [← zero_mk s, mk_add_mk, smul_zero, zero_add, mk_eq] <;>
         exact ⟨1, by rw [one_smul, mul_smul, one_smul]⟩)
     x
-#align localized_module.zero_add' localized_module.zero_add'
 
 private theorem add_zero' (x : LocalizedModule S M) : x + 0 = x :=
   induction_on
@@ -282,7 +261,6 @@ private theorem add_zero' (x : LocalizedModule S M) : x + 0 = x :=
       rw [← zero_mk s, mk_add_mk, smul_zero, add_zero, mk_eq] <;>
         exact ⟨1, by rw [one_smul, mul_smul, one_smul]⟩)
     x
-#align localized_module.add_zero' localized_module.add_zero'
 
 #print LocalizedModule.hasNatSmul /-
 instance hasNatSmul : SMul ℕ (LocalizedModule S M) where smul n := nsmulRec n
@@ -291,11 +269,9 @@ instance hasNatSmul : SMul ℕ (LocalizedModule S M) where smul n := nsmulRec n
 
 private theorem nsmul_zero' (x : LocalizedModule S M) : (0 : ℕ) • x = 0 :=
   LocalizedModule.induction_on (fun _ _ => rfl) x
-#align localized_module.nsmul_zero' localized_module.nsmul_zero'
 
 private theorem nsmul_succ' (n : ℕ) (x : LocalizedModule S M) : n.succ • x = x + n • x :=
   LocalizedModule.induction_on (fun _ _ => rfl) x
-#align localized_module.nsmul_succ' localized_module.nsmul_succ'
 
 instance : AddCommMonoid (LocalizedModule S M)
     where
@@ -425,10 +401,7 @@ instance {A : Type _} [CommRing A] [Algebra R A] {S : Submonoid R} :
       exact mk_eq.mpr ⟨1, by simp only [one_smul, mul_comm]⟩ }
 
 /- warning: localized_module.mk_mul_mk -> LocalizedModule.mk_mul_mk is a dubious translation:
-lean 3 declaration is
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s₁ s₂))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.mk_mul_mk LocalizedModule.mk_mul_mkₓ'. -/
 theorem mk_mul_mk {A : Type _} [Semiring A] [Algebra R A] {a₁ a₂ : A} {s₁ s₂ : S} :
     mk a₁ s₁ * mk a₂ s₂ = mk (a₁ * a₂) (s₁ * s₂) :=
@@ -459,10 +432,7 @@ instance : SMul (Localization S) (LocalizedModule S M)
         rw [eq1'])
 
 /- warning: localized_module.mk_smul_mk -> LocalizedModule.mk_smul_mk is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align localized_module.mk_smul_mk LocalizedModule.mk_smul_mkₓ'. -/
 theorem mk_smul_mk (r : R) (m : M) (s t : S) : Localization.mk r s • mk m t = mk (r • m) (s * t) :=
   by
@@ -474,7 +444,6 @@ private theorem one_smul' (m : LocalizedModule S M) : (1 : Localization S) • m
   by
   induction' m using LocalizedModule.induction_on with m s
   rw [← Localization.mk_one, mk_smul_mk, one_smul, one_mul]
-#align localized_module.one_smul' localized_module.one_smul'
 
 private theorem mul_smul' (x y : Localization S) (m : LocalizedModule S M) :
     (x * y) • m = x • y • m :=
@@ -484,7 +453,6 @@ private theorem mul_smul' (x y : Localization S) (m : LocalizedModule S M) :
   rcases data, data' with ⟨⟨r, s⟩, ⟨r', s'⟩⟩
   induction' m using LocalizedModule.induction_on with m t
   rw [Localization.mk_mul, mk_smul_mk, mk_smul_mk, mk_smul_mk, mul_smul, mul_assoc]
-#align localized_module.mul_smul' localized_module.mul_smul'
 
 private theorem smul_add' (x : Localization S) (y z : LocalizedModule S M) :
     x • (y + z) = x • y + x • z :=
@@ -497,14 +465,12 @@ private theorem smul_add' (x : Localization S) (y z : LocalizedModule S M) :
   use 1
   simp only [one_smul, smul_add, ← mul_smul, Submonoid.smul_def, Submonoid.coe_mul]
   ring_nf
-#align localized_module.smul_add' localized_module.smul_add'
 
 private theorem smul_zero' (x : Localization S) : x • (0 : LocalizedModule S M) = 0 :=
   by
   induction' x using Localization.induction_on with data
   rcases data with ⟨r, s⟩
   rw [← zero_mk s, mk_smul_mk, smul_zero, zero_mk, zero_mk]
-#align localized_module.smul_zero' localized_module.smul_zero'
 
 private theorem add_smul' (x y : Localization S) (z : LocalizedModule S M) :
     (x + y) • z = x • z + y • z :=
@@ -520,13 +486,11 @@ private theorem add_smul' (x y : Localization S) (z : LocalizedModule S M) :
   rw [add_comm]
   -- Commutativity of addition in the module is not applied by `ring`.
   ring_nf
-#align localized_module.add_smul' localized_module.add_smul'
 
 private theorem zero_smul' (x : LocalizedModule S M) : (0 : Localization S) • x = 0 :=
   by
   induction' x using LocalizedModule.induction_on with m s
   rw [← Localization.mk_zero s, mk_smul_mk, zero_smul, zero_mk]
-#align localized_module.zero_smul' localized_module.zero_smul'
 
 /- warning: localized_module.is_module -> LocalizedModule.isModule is a dubious translation:
 lean 3 declaration is
@@ -546,10 +510,7 @@ instance isModule : Module (Localization S) (LocalizedModule S M)
 #align localized_module.is_module LocalizedModule.isModule
 
 /- warning: localized_module.mk_cancel_common_left -> LocalizedModule.mk_cancel_common_left is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.mk_cancel_common_left LocalizedModule.mk_cancel_common_leftₓ'. -/
 @[simp]
 theorem mk_cancel_common_left (s' s : S) (m : M) : mk (s' • m) (s' * s) = mk m s :=
@@ -560,10 +521,7 @@ theorem mk_cancel_common_left (s' s : S) (m : M) : mk (s' • m) (s' * s) = mk m
 #align localized_module.mk_cancel_common_left LocalizedModule.mk_cancel_common_left
 
 /- warning: localized_module.mk_cancel -> LocalizedModule.mk_cancel is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align localized_module.mk_cancel LocalizedModule.mk_cancelₓ'. -/
 @[simp]
 theorem mk_cancel (s : S) (m : M) : mk (s • m) s = mk m 1 :=
@@ -571,10 +529,7 @@ theorem mk_cancel (s : S) (m : M) : mk (s • m) s = mk m 1 :=
 #align localized_module.mk_cancel LocalizedModule.mk_cancel
 
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s s')) (LocalizedModule.mk.{u1, u2} R _inst_1 S M _inst_2 _inst_3 m s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.mk_cancel_common_right LocalizedModule.mk_cancel_common_rightₓ'. -/
 @[simp]
 theorem mk_cancel_common_right (s s' : S) (m : M) : mk (s' • m) (s * s') = mk m s :=
@@ -619,10 +574,7 @@ instance {A : Type _} [Semiring A] [Algebra R A] : Algebra (Localization S) (Loc
         mul_smul_comm])
 
 /- warning: localized_module.algebra_map_mk -> LocalizedModule.algebraMap_mk is a dubious translation:
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R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) 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A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S))) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} 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(LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S)) (RingHom.instRingHomClassRingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.algebra_map_mk LocalizedModule.algebraMap_mkₓ'. -/
 theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
     algebraMap _ _ (Localization.mk a s) = mk (algebraMap R A a) s :=
@@ -713,10 +665,7 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M
 #align localized_module.div_by LocalizedModule.divBy
 
 /- warning: localized_module.div_by_mul_by -> LocalizedModule.divBy_mul_by is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.div_by_mul_by LocalizedModule.divBy_mul_byₓ'. -/
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
     divBy s (algebraMap R (Module.End R (LocalizedModule S M)) s p) = p :=
@@ -728,10 +677,7 @@ theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
 #align localized_module.div_by_mul_by LocalizedModule.divBy_mul_by
 
 /- warning: localized_module.mul_by_div_by -> LocalizedModule.mul_by_divBy is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.mul_by_div_by LocalizedModule.mul_by_divByₓ'. -/
 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
     algebraMap R (Module.End R (LocalizedModule S M)) s (divBy s p) = p :=
@@ -774,10 +720,7 @@ class IsLocalizedModule : Prop where
 namespace LocalizedModule
 
 /- warning: localized_module.lift' -> LocalizedModule.lift' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift' LocalizedModule.lift'ₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -814,10 +757,7 @@ noncomputable def lift' (g : M →ₗ[R] M'')
 #align localized_module.lift' LocalizedModule.lift'
 
 /- warning: localized_module.lift'_mk -> LocalizedModule.lift'_mk is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift'_mk LocalizedModule.lift'_mkₓ'. -/
 theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (m : M) (s : S) : LocalizedModule.lift' S g h (LocalizedModule.mk m s) = (h s).Unit⁻¹.1 (g m) :=
@@ -825,10 +765,7 @@ theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Mo
 #align localized_module.lift'_mk LocalizedModule.lift'_mk
 
 /- warning: localized_module.lift'_add -> LocalizedModule.lift'_add is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift'_add LocalizedModule.lift'_addₓ'. -/
 theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (x y) :
@@ -848,10 +785,7 @@ theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
 #align localized_module.lift'_add LocalizedModule.lift'_add
 
 /- warning: localized_module.lift'_smul -> LocalizedModule.lift'_smul is a dubious translation:
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-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift'_smul LocalizedModule.lift'_smulₓ'. -/
 theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (r : R) (m) : r • LocalizedModule.lift' S g h m = LocalizedModule.lift' S g h (r • m) :=
@@ -864,10 +798,7 @@ theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (
 #align localized_module.lift'_smul LocalizedModule.lift'_smul
 
 /- warning: localized_module.lift -> LocalizedModule.lift is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift LocalizedModule.liftₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -882,10 +813,7 @@ noncomputable def lift (g : M →ₗ[R] M'')
 #align localized_module.lift LocalizedModule.lift
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift_mk LocalizedModule.lift_mkₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -897,10 +825,7 @@ theorem lift_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Mod
 #align localized_module.lift_mk LocalizedModule.lift_mk
 
 /- warning: localized_module.lift_comp -> LocalizedModule.lift_comp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift_comp LocalizedModule.lift_compₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -914,10 +839,7 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
 #align localized_module.lift_comp LocalizedModule.lift_comp
 
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(Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (l : LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7), (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u3, u3, u3, u2, max u3 u2, u1} R R R M (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 _inst_5 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align localized_module.lift_unique LocalizedModule.lift_uniqueₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible and
@@ -987,10 +909,7 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
 -/
 
 /- warning: is_localized_module.from_localized_module'_mk -> IsLocalizedModule.fromLocalizedModule'_mk is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_mk IsLocalizedModule.fromLocalizedModule'_mkₓ'. -/
 @[simp]
 theorem fromLocalizedModule'_mk (m : M) (s : S) :
@@ -1026,10 +945,7 @@ theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
 #align is_localized_module.from_localized_module'_add IsLocalizedModule.fromLocalizedModule'_add
 
 /- warning: is_localized_module.from_localized_module'_smul -> IsLocalizedModule.fromLocalizedModule'_smul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_smul IsLocalizedModule.fromLocalizedModule'_smulₓ'. -/
 theorem fromLocalizedModule'_smul (r : R) (x : LocalizedModule S M) :
     r • fromLocalizedModule' S f x = fromLocalizedModule' S f (r • x) :=
@@ -1058,10 +974,7 @@ noncomputable def fromLocalizedModule : LocalizedModule S M →ₗ[R] M'
 #align is_localized_module.from_localized_module IsLocalizedModule.fromLocalizedModule
 
 /- warning: is_localized_module.from_localized_module_mk -> IsLocalizedModule.fromLocalizedModule_mk is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module_mk IsLocalizedModule.fromLocalizedModule_mkₓ'. -/
 theorem fromLocalizedModule_mk (m : M) (s : S) :
     fromLocalizedModule S f (LocalizedModule.mk m s) =
@@ -1128,10 +1041,7 @@ noncomputable def iso : LocalizedModule S M ≃ₗ[R] M' :=
 #align is_localized_module.iso IsLocalizedModule.iso
 
 /- warning: is_localized_module.iso_apply_mk -> IsLocalizedModule.iso_apply_mk is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_apply_mk IsLocalizedModule.iso_apply_mkₓ'. -/
 theorem iso_apply_mk (m : M) (s : S) :
     iso S f (LocalizedModule.mk m s) = (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
@@ -1139,10 +1049,7 @@ theorem iso_apply_mk (m : M) (s : S) :
 #align is_localized_module.iso_apply_mk IsLocalizedModule.iso_apply_mk
 
 /- warning: is_localized_module.iso_symm_apply_aux -> IsLocalizedModule.iso_symm_apply_aux is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_apply_aux IsLocalizedModule.iso_symm_apply_auxₓ'. -/
 theorem iso_symm_apply_aux (m : M') :
     (iso S f).symm m =
@@ -1157,10 +1064,7 @@ theorem iso_symm_apply_aux (m : M') :
 #align is_localized_module.iso_symm_apply_aux IsLocalizedModule.iso_symm_apply_aux
 
 /- warning: is_localized_module.iso_symm_apply' -> IsLocalizedModule.iso_symm_apply' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'ₓ'. -/
 theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
     (iso S f).symm m = LocalizedModule.mk a b :=
@@ -1172,10 +1076,7 @@ theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
 #align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_comp IsLocalizedModule.iso_symm_compₓ'. -/
 theorem iso_symm_comp : (iso S f).symm.toLinearMap.comp f = LocalizedModule.mkLinearMap S M :=
   by
@@ -1184,10 +1085,7 @@ theorem iso_symm_comp : (iso S f).symm.toLinearMap.comp f = LocalizedModule.mkLi
 #align is_localized_module.iso_symm_comp IsLocalizedModule.iso_symm_comp
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.lift IsLocalizedModule.liftₓ'. -/
 /--
 If `M'` is a localized module and `g` is a linear map `M' → M''` such that all scalar multiplication
@@ -1199,10 +1097,7 @@ noncomputable def lift (g : M →ₗ[R] M'')
 #align is_localized_module.lift IsLocalizedModule.lift
 
 /- warning: is_localized_module.lift_comp -> IsLocalizedModule.lift_comp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.lift_comp IsLocalizedModule.lift_compₓ'. -/
 theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x)) :
     (lift S f g h).comp f = g :=
@@ -1214,10 +1109,7 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
 #align is_localized_module.lift_comp IsLocalizedModule.lift_comp
 
 /- warning: is_localized_module.lift_unique -> IsLocalizedModule.lift_unique is a dubious translation:
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_inst_5 _inst_6 _inst_7 f _inst_8 g h) l)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.lift_unique IsLocalizedModule.lift_uniqueₓ'. -/
 theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (l : M' →ₗ[R] M'') (hl : l.comp f = g) : lift S f g h = l :=
@@ -1234,10 +1126,7 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
 #align is_localized_module.lift_unique IsLocalizedModule.lift_unique
 
 /- warning: is_localized_module.is_universal -> IsLocalizedModule.is_universal is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.is_universal IsLocalizedModule.is_universalₓ'. -/
 /-- Universal property from localized module:
 If `(M', f : M ⟶ M')` is a localized module then it satisfies the following universal property:
@@ -1260,10 +1149,7 @@ theorem is_universal :
 #align is_localized_module.is_universal IsLocalizedModule.is_universal
 
 /- warning: is_localized_module.ring_hom_ext -> IsLocalizedModule.ringHom_ext is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localized_module.ring_hom_ext IsLocalizedModule.ringHom_extₓ'. -/
 theorem ringHom_ext (map_unit : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     ⦃j k : M' →ₗ[R] M''⦄ (h : j.comp f = k.comp f) : j = k :=
@@ -1284,20 +1170,14 @@ noncomputable def linearEquiv [IsLocalizedModule S g] : M' ≃ₗ[R] M'' :=
 variable {S}
 
 /- warning: is_localized_module.smul_injective -> IsLocalizedModule.smul_injective is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localized_module.smul_injective IsLocalizedModule.smul_injectiveₓ'. -/
 theorem smul_injective (s : S) : Function.Injective fun m : M' => s • m :=
   ((Module.End_isUnit_iff _).mp (IsLocalizedModule.map_units f s)).Injective
 #align is_localized_module.smul_injective IsLocalizedModule.smul_injective
 
 /- warning: is_localized_module.smul_inj -> IsLocalizedModule.smul_inj is a dubious translation:
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(Eq.{succ u1} M' m₁ m₂)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.smul_inj IsLocalizedModule.smul_injₓ'. -/
 theorem smul_inj (s : S) (m₁ m₂ : M') : s • m₁ = s • m₂ ↔ m₁ = m₂ :=
   (smul_injective f s).eq_iff
@@ -1315,10 +1195,7 @@ noncomputable def mk' (m : M) (s : S) : M' :=
 #align is_localized_module.mk' IsLocalizedModule.mk'
 
 /- warning: is_localized_module.mk'_smul -> IsLocalizedModule.mk'_smul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_smul IsLocalizedModule.mk'_smulₓ'. -/
 theorem mk'_smul (r : R) (m : M) (s : S) : mk' f (r • m) s = r • mk' f m s :=
   by
@@ -1327,10 +1204,7 @@ theorem mk'_smul (r : R) (m : M) (s : S) : mk' f (r • m) s = r • mk' f m s :
 #align is_localized_module.mk'_smul IsLocalizedModule.mk'_smul
 
 /- warning: is_localized_module.mk'_add_mk' -> IsLocalizedModule.mk'_add_mk' is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_add_mk' IsLocalizedModule.mk'_add_mk'ₓ'. -/
 theorem mk'_add_mk' (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ + mk' f m₂ s₂ = mk' f (s₂ • m₁ + s₁ • m₂) (s₁ * s₂) :=
@@ -1352,10 +1226,7 @@ theorem mk'_zero (s : S) : mk' f 0 s = 0 := by rw [← zero_smul R (0 : M), mk'_
 variable (S)
 
 /- warning: is_localized_module.mk'_one -> IsLocalizedModule.mk'_one is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_one IsLocalizedModule.mk'_oneₓ'. -/
 @[simp]
 theorem mk'_one (m : M) : mk' f m (1 : S) = f m :=
@@ -1368,10 +1239,7 @@ theorem mk'_one (m : M) : mk' f m (1 : S) = f m :=
 variable {S}
 
 /- warning: is_localized_module.mk'_cancel -> IsLocalizedModule.mk'_cancel is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancelₓ'. -/
 @[simp]
 theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m :=
@@ -1382,10 +1250,7 @@ theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m :=
 #align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancel
 
 /- warning: is_localized_module.mk'_cancel' -> IsLocalizedModule.mk'_cancel' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel' IsLocalizedModule.mk'_cancel'ₓ'. -/
 @[simp]
 theorem mk'_cancel' (m : M) (s : S) : s • mk' f m s = f m := by
@@ -1393,10 +1258,7 @@ theorem mk'_cancel' (m : M) (s : S) : s • mk' f m s = f m := by
 #align is_localized_module.mk'_cancel' IsLocalizedModule.mk'_cancel'
 
 /- warning: is_localized_module.mk'_cancel_left -> IsLocalizedModule.mk'_cancel_left is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel_left IsLocalizedModule.mk'_cancel_leftₓ'. -/
 @[simp]
 theorem mk'_cancel_left (m : M) (s₁ s₂ : S) : mk' f (s₁ • m) (s₁ * s₂) = mk' f m s₂ :=
@@ -1406,10 +1268,7 @@ theorem mk'_cancel_left (m : M) (s₁ s₂ : S) : mk' f (s₁ • m) (s₁ * s
 #align is_localized_module.mk'_cancel_left IsLocalizedModule.mk'_cancel_left
 
 /- warning: is_localized_module.mk'_cancel_right -> IsLocalizedModule.mk'_cancel_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel_right IsLocalizedModule.mk'_cancel_rightₓ'. -/
 @[simp]
 theorem mk'_cancel_right (m : M) (s₁ s₂ : S) : mk' f (s₂ • m) (s₁ * s₂) = mk' f m s₁ :=
@@ -1429,10 +1288,7 @@ theorem mk'_add (m₁ m₂ : M) (s : S) : mk' f (m₁ + m₂) s = mk' f m₁ s +
 #align is_localized_module.mk'_add IsLocalizedModule.mk'_add
 
 /- warning: is_localized_module.mk'_eq_mk'_iff -> IsLocalizedModule.mk'_eq_mk'_iff is a dubious translation:
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_mk'_iff IsLocalizedModule.mk'_eq_mk'_iffₓ'. -/
 theorem mk'_eq_mk'_iff (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ = mk' f m₂ s₂ ↔ ∃ s : S, s • s₁ • m₂ = s • s₂ • m₁ :=
@@ -1468,10 +1324,7 @@ theorem mk'_sub {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M]
 #align is_localized_module.mk'_sub IsLocalizedModule.mk'_sub
 
 /- warning: is_localized_module.mk'_sub_mk' -> IsLocalizedModule.mk'_sub_mk' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_sub_mk' IsLocalizedModule.mk'_sub_mk'ₓ'. -/
 theorem mk'_sub_mk' {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
@@ -1480,10 +1333,7 @@ theorem mk'_sub_mk' {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R
 #align is_localized_module.mk'_sub_mk' IsLocalizedModule.mk'_sub_mk'
 
 /- warning: is_localized_module.mk'_mul_mk'_of_map_mul -> IsLocalizedModule.mk'_mul_mk'_of_map_mul is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_mul_mk'_of_map_mul IsLocalizedModule.mk'_mul_mk'_of_map_mulₓ'. -/
 theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Module R M]
     [Algebra R M'] (f : M →ₗ[R] M') (hf : ∀ m₁ m₂, f (m₁ * m₂) = f m₁ * f m₂)
@@ -1498,10 +1348,7 @@ theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Modul
 #align is_localized_module.mk'_mul_mk'_of_map_mul IsLocalizedModule.mk'_mul_mk'_of_map_mul
 
 /- warning: is_localized_module.mk'_mul_mk' -> IsLocalizedModule.mk'_mul_mk' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_mul_mk' IsLocalizedModule.mk'_mul_mk'ₓ'. -/
 theorem mk'_mul_mk' {M M' : Type _} [Semiring M] [Semiring M'] [Algebra R M] [Algebra R M']
     (f : M →ₐ[R] M') [IsLocalizedModule S f.toLinearMap] (m₁ m₂ : M) (s₁ s₂ : S) :
@@ -1512,10 +1359,7 @@ theorem mk'_mul_mk' {M M' : Type _} [Semiring M] [Semiring M'] [Algebra R M] [Al
 variable {f}
 
 /- warning: is_localized_module.mk'_eq_iff -> IsLocalizedModule.mk'_eq_iff is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_iff IsLocalizedModule.mk'_eq_iffₓ'. -/
 @[simp]
 theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m' := by
@@ -1523,10 +1367,7 @@ theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m'
 #align is_localized_module.mk'_eq_iff IsLocalizedModule.mk'_eq_iff
 
 /- warning: is_localized_module.mk'_eq_zero -> IsLocalizedModule.mk'_eq_zero is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_zero IsLocalizedModule.mk'_eq_zeroₓ'. -/
 @[simp]
 theorem mk'_eq_zero {m : M} (s : S) : mk' f m s = 0 ↔ f m = 0 := by rw [mk'_eq_iff, smul_zero]
@@ -1535,10 +1376,7 @@ theorem mk'_eq_zero {m : M} (s : S) : mk' f m s = 0 ↔ f m = 0 := by rw [mk'_eq
 variable (f)
 
 /- warning: is_localized_module.mk'_eq_zero' -> IsLocalizedModule.mk'_eq_zero' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_zero' IsLocalizedModule.mk'_eq_zero'ₓ'. -/
 theorem mk'_eq_zero' {m : M} (s : S) : mk' f m s = 0 ↔ ∃ s' : S, s' • m = 0 := by
   simp_rw [← mk'_zero f (1 : S), mk'_eq_mk'_iff, smul_zero, one_smul, eq_comm]
@@ -1559,10 +1397,7 @@ theorem mk_eq_mk' (s : S) (m : M) :
 variable (S)
 
 /- warning: is_localized_module.eq_zero_iff -> IsLocalizedModule.eq_zero_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.eq_zero_iff IsLocalizedModule.eq_zero_iffₓ'. -/
 theorem eq_zero_iff {m : M} : f m = 0 ↔ ∃ s' : S, s' • m = 0 :=
   (mk'_eq_zero (1 : S)).symm.trans (mk'_eq_zero' f _)
@@ -1584,10 +1419,7 @@ theorem mk'_surjective : Function.Surjective (Function.uncurry <| mk' f : M × S
 section Algebra
 
 /- warning: is_localized_module.mk_of_algebra -> IsLocalizedModule.mkOfAlgebra is a dubious translation:
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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12)) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R S S' (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHomClass.linearMapClass.{u3, u2, u1, max u2 u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (AlgHom.algHomClass.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13))))) f x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') x) _inst_11)))))) -> (Exists.{succ u3} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) (fun (m : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) => Eq.{succ u2} S (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S S (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S (Submonoid.smul.{u3, u2} R S (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (Algebra.toSMul.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) M)) m x) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))))) -> (IsLocalizedModule.{u3, u2, u1} R _inst_9 M S S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHom.toLinearMap.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk_of_algebra IsLocalizedModule.mkOfAlgebraₓ'. -/
 theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [Algebra R S]
     [Algebra R S'] (M : Submonoid R) (f : S →ₐ[R] S') (h₁ : ∀ x ∈ M, IsUnit (algebraMap R S' x))

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

@@ -716,7 +716,7 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S) (p : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3), Eq.{succ (max u1 u2)} (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) => (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) -> (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LocalizedModule.divBy.{u1, u2} R _inst_1 S M _inst_2 _inst_3 s) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) => (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) -> (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max 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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))))))) (algebraMap.{u1, max u2 u1} R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) _inst_1 (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.instAlgebraEndToSemiringSemiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _inst_1 (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) S)) s)) p)) p
 Case conversion may be inaccurate. Consider using '#align localized_module.div_by_mul_by LocalizedModule.divBy_mul_byₓ'. -/
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
     divBy s (algebraMap R (Module.End R (LocalizedModule S M)) s p) = p :=
@@ -731,7 +731,7 @@ theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S) (p : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3), Eq.{succ (max u1 u2)} (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) => (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) -> (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (RingHom.{u1, max u1 u2} R (Module.End.{u1, max u1 u2} R 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 but is expected to have type
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(LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))))))) (algebraMap.{u1, max u2 u1} R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) _inst_1 (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.instAlgebraEndToSemiringSemiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _inst_1 (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (fun (_x : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) => LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LocalizedModule.divBy.{u1, u2} R _inst_1 S M _inst_2 _inst_3 s) p)) p
 Case conversion may be inaccurate. Consider using '#align localized_module.mul_by_div_by LocalizedModule.mul_by_divByₓ'. -/
 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
     algebraMap R (Module.End R (LocalizedModule S M)) s (divBy s p) = p :=
@@ -817,7 +817,7 @@ noncomputable def lift' (g : M →ₗ[R] M'')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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_inst_7 _inst_7) => M'' -> M'') (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M'' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_4 _inst_7 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Units.val.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Inv.inv.{u3} (Units.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (Units.hasInv.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (h s)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) => M -> M'') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) g m))
 but is expected to have type
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(x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, 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(Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, 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(Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u1} M'' (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (LocalizedModule.mk.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u1} R R M'' M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_4 _inst_7 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Inv.inv.{u1} (Units.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (Units.instInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (IsUnit.unit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
 Case conversion may be inaccurate. Consider using '#align localized_module.lift'_mk LocalizedModule.lift'_mkₓ'. -/
 theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (m : M) (s : S) : LocalizedModule.lift' S g h (LocalizedModule.mk m s) = (h s).Unit⁻¹.1 (g m) :=
@@ -885,7 +885,7 @@ noncomputable def lift (g : M →ₗ[R] M'')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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_inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} 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 but is expected to have type
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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (m : M) (s : Subtype.{succ u3} R 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 Case conversion may be inaccurate. Consider using '#align localized_module.lift_mk LocalizedModule.lift_mkₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -990,7 +990,7 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (IsLocalizedModule.fromLocalizedModule'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (LocalizedModule.mk.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5 m s)) (coeFn.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (fun (x : Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) => M' -> M') (coeFnTrans.{succ u3, succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M' _inst_3 _inst_3 _inst_6 _inst_6) => M' -> M') (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M' M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeBaseAux.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Units.hasCoe.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) (Inv.inv.{u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Units.hasInv.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) => R -> (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.algebra.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_3 _inst_6)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (IsLocalizedModule.map_units.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.fromLocalizedModule'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M' (fun (x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M') => M') x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M' M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Inv.inv.{u2} (Units.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (Units.instInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.fromLocalizedModule'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M' (fun (x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M') => M') x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M' M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Inv.inv.{u2} (Units.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (Units.instInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' 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(Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_mk IsLocalizedModule.fromLocalizedModule'_mkₓ'. -/
 @[simp]
 theorem fromLocalizedModule'_mk (m : M) (s : S) :
@@ -1061,7 +1061,7 @@ noncomputable def fromLocalizedModule : LocalizedModule S M →ₗ[R] M'
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ 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 but is expected to have type
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(CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') 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_inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M' (fun (x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M') => M') x) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (Units.instInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R 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(Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module_mk IsLocalizedModule.fromLocalizedModule_mkₓ'. -/
 theorem fromLocalizedModule_mk (m : M) (s : S) :
     fromLocalizedModule S f (LocalizedModule.mk m s) =
@@ -1073,7 +1073,7 @@ theorem fromLocalizedModule_mk (m : M) (s : S) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Injective.{succ (max u1 u2), succ u3} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Injective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Injective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.injₓ'. -/
 theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f := fun x y eq1 =>
   by
@@ -1091,7 +1091,7 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Surjective.{succ (max u1 u2), succ u3} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Surjective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Surjective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.surj IsLocalizedModule.fromLocalizedModule.surjₓ'. -/
 theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S f := fun x =>
   let ⟨⟨m, s⟩, eq1⟩ := IsLocalizedModule.surj S f x
@@ -1105,7 +1105,7 @@ theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Bijective.{succ (max u1 u2), succ u3} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Bijective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Bijective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.bij IsLocalizedModule.fromLocalizedModule.bijₓ'. -/
 theorem fromLocalizedModule.bij : Function.Bijective <| fromLocalizedModule S f :=
   ⟨fromLocalizedModule.inj _ _, fromLocalizedModule.surj _ _⟩
@@ -1131,7 +1131,7 @@ noncomputable def iso : LocalizedModule S M ≃ₗ[R] M' :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ 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(IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearEquiv.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1)) (IsLocalizedModule.iso.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8) (LocalizedModule.mk.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5 m s)) (coeFn.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (fun (x : Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) 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R _inst_1))))) (coeBaseAux.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Units.hasCoe.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) (Inv.inv.{u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Units.hasInv.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) => R -> (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.algebra.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_3 _inst_6)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (IsLocalizedModule.map_units.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') 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(CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (SMulZeroClass.toSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R 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(Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u3, max u3 u1, u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R 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(CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (SemilinearMapClass.distribMulActionHomClass.{u3, max u3 u1, u2, max (max u3 u1) u2} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) 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(CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (IsLocalizedModule.iso.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M' (fun (x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M') => M') x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M' M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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(MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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_inst_1)) _inst_3 _inst_6) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), succ u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u3, max u3 u1, u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (SMulZeroClass.toSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R 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(Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_apply_mk IsLocalizedModule.iso_apply_mkₓ'. -/
 theorem iso_apply_mk (m : M) (s : S) :
     iso S f (LocalizedModule.mk m s) = (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
@@ -1142,7 +1142,7 @@ theorem iso_apply_mk (m : M) (s : S) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M'), Eq.{succ (max u1 u2)} 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_inst_2 _inst_5) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R 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(CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) x) m) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f (Prod.fst.{u2, u1} M (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) x))) (IsLocalizedModule.surj.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M'), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M') => LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) m) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearEquiv.{u3, u3, u1, max u3 u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M') => LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u3, u1, max u3 u2} (LinearEquiv.{u3, u3, u1, max u3 u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toSMul.{u3, u1} R M' (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u1} R M' (AddMonoid.toAddZeroClass.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (DistribMulAction.toDistribSMul.{u3, u1} R M' (MonoidWithZero.toMonoid.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f (Prod.fst.{u2, u3} M (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R 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+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R 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 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_apply_aux IsLocalizedModule.iso_symm_apply_auxₓ'. -/
 theorem iso_symm_apply_aux (m : M') :
     (iso S f).symm m =
@@ -1160,7 +1160,7 @@ theorem iso_symm_apply_aux (m : M') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M') (a : M) (b : coeSort.{succ u1, 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u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (Submonoid.hasSmul.{u1, u3} R M' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) S) b m) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) (fun (_x : LinearEquiv.{u1, u1, u3, max u1 u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) => M' -> (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max u1 u2} R R M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8)) m) (LocalizedModule.mk.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5 a b))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M') (a : M) (b : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), (Eq.{succ u2} M' (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) b m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f a)) -> (Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M') => LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) m) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u2, max (succ u3) (succ u1)} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M') => LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u3, u2, max u3 u1} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M' (AddMonoid.toAddZeroClass.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u3, u2, max u3 u1} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, max u3 u1, max (max u3 u1) u2} R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, max u3 u1, max (max u3 u1) u2} R R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, max u3 u1} R R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearEquiv.symm.{u3, u3, max u3 u1, u2} R R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IsLocalizedModule.iso.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8)) m) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 a b))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M') (a : M) (b : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), (Eq.{succ u2} M' (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) b m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f a)) -> (Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M') => LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) m) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u2, max (succ u3) (succ u1)} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M') => LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u3, u2, max u3 u1} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) 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(DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u3, u2, max u3 u1} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, max u3 u1, max (max u3 u1) u2} R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, max u3 u1, max (max u3 u1) u2} R R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, max u3 u1} R R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearEquiv.symm.{u3, u3, max u3 u1, u2} R R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IsLocalizedModule.iso.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8)) m) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 a b))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'ₓ'. -/
 theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
     (iso S f).symm m = LocalizedModule.mk a b :=
@@ -1355,7 +1355,7 @@ variable (S)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M), Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) S))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2] [_inst_6 : Module.{u2, u3} R M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3] (f : LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u2, u1, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M), Eq.{succ u3} M' (IsLocalizedModule.mk'.{u2, u1, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m (OfNat.ofNat.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) 1 (One.toOfNat1.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) (Submonoid.one.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) S)))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R M M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f m)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2] [_inst_6 : Module.{u2, u3} R M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3] (f : LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u2, u1, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M), Eq.{succ u3} M' (IsLocalizedModule.mk'.{u2, u1, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m (OfNat.ofNat.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) 1 (One.toOfNat1.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) (Submonoid.one.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) S)))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R M M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f m)
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_one IsLocalizedModule.mk'_oneₓ'. -/
 @[simp]
 theorem mk'_one (m : M) : mk' f m (1 : S) = f m :=
@@ -1371,7 +1371,7 @@ variable {S}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M (Submonoid.hasSmul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_5)))) S) s m) s) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (HSMul.hSMul.{u3, u1, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M M (instHSMul.{u3, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M (Submonoid.smul.{u3, u1} R M (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_5)))) S)) s m) s) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m)
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (HSMul.hSMul.{u3, u1, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M M (instHSMul.{u3, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M (Submonoid.smul.{u3, u1} R M (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_5)))) S)) s m) s) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m)
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancelₓ'. -/
 @[simp]
 theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m :=
@@ -1385,7 +1385,7 @@ theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (SMul.smul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (Submonoid.hasSmul.{u1, u3} R M' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) S) s (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) s (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m)
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) s (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m)
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel' IsLocalizedModule.mk'_cancel'ₓ'. -/
 @[simp]
 theorem mk'_cancel' (m : M) (s : S) : s • mk' f m s = f m := by
@@ -1483,7 +1483,7 @@ theorem mk'_sub_mk' {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_9 : Semiring.{u2} M] [_inst_10 : Semiring.{u3} M'] [_inst_11 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9)))] [_inst_12 : Algebra.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)), (forall (m₁ : M) (m₂ : M), Eq.{succ u3} M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f (HMul.hMul.{u2, u2, u2} M M M (instHMul.{u2} M (Distrib.toHasMul.{u2} M (NonUnitalNonAssocSemiring.toDistrib.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))))) m₁ m₂)) (HMul.hMul.{u3, u3, u3} M' M' M' (instHMul.{u3} M' (Distrib.toHasMul.{u3} M' (NonUnitalNonAssocSemiring.toDistrib.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))))) (coeFn.{max 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m₁) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m₂))) -> (forall [_inst_13 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f] (m₁ : M) (m₂ : M) (s₁ : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (s₂ : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (HMul.hMul.{u3, u3, u3} M' M' M' (instHMul.{u3} M' (Distrib.toHasMul.{u3} M' (NonUnitalNonAssocSemiring.toDistrib.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))))) (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₁ s₁) (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₂ s₂)) (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 (HMul.hMul.{u2, u2, u2} M M M (instHMul.{u2} M (Distrib.toHasMul.{u2} M (NonUnitalNonAssocSemiring.toDistrib.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))))) m₁ m₂) (HMul.hMul.{u1, u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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(NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (instHMul.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (Submonoid.mul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) S)) s₁ s₂)))
 but is expected to have type
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(CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)), (forall (m₁ : M) (m₂ : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m₁) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m₂) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m₁) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m₁) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 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(CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m₁) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m₂))) -> (forall [_inst_13 : IsLocalizedModule.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f] (m₁ : M) (m₂ : M) (s₁ : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (s₂ : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), Eq.{succ u2} M' (HMul.hMul.{u2, u2, u2} M' M' M' (instHMul.{u2} M' (NonUnitalNonAssocSemiring.toMul.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10)))) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₁ s₁) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₂ s₂)) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂) (HMul.hMul.{u1, u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (instHMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (Submonoid.mul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) S)) s₁ s₂)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {M : Type.{u3}} {M' : Type.{u2}} [_inst_9 : Semiring.{u3} M] [_inst_10 : Semiring.{u2} M'] [_inst_11 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))] [_inst_12 : Algebra.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)), (forall (m₁ : M) (m₂ : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m₂))) -> (forall [_inst_13 : IsLocalizedModule.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f] (m₁ : M) (m₂ : M) (s₁ : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (s₂ : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), Eq.{succ u2} M' (HMul.hMul.{u2, u2, u2} M' M' M' (instHMul.{u2} M' (NonUnitalNonAssocSemiring.toMul.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10)))) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₁ s₁) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₂ s₂)) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂) (HMul.hMul.{u1, u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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_inst_1))))))) x S)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (instHMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (Submonoid.mul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) S)) s₁ s₂)))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_mul_mk'_of_map_mul IsLocalizedModule.mk'_mul_mk'_of_map_mulₓ'. -/
 theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Module R M]
     [Algebra R M'] (f : M →ₗ[R] M') (hf : ∀ m₁ m₂, f (m₁ * m₂) = f m₁ * f m₂)
@@ -1515,7 +1515,7 @@ variable {f}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] {f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} {s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S} {m' : M'}, Iff (Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) m') (Eq.{succ u3} M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m) (SMul.smul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (Submonoid.hasSmul.{u1, u3} R M' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) S) s m'))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] {f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} {s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)} {m' : M'}, Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) m') (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m) (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) s m'))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] {f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} {s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)} {m' : M'}, Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) m') (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m) (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) s m'))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_iff IsLocalizedModule.mk'_eq_iffₓ'. -/
 @[simp]
 theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m' := by
@@ -1526,7 +1526,7 @@ theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m'
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] {f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Iff (Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) (OfNat.ofNat.{u3} M' 0 (OfNat.mk.{u3} M' 0 (Zero.zero.{u3} M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))))))) (Eq.{succ u3} M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m) (OfNat.ofNat.{u3} M' 0 (OfNat.mk.{u3} M' 0 (Zero.zero.{u3} M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3)))))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] {f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) (OfNat.ofNat.{u2} M' 0 (Zero.toOfNat0.{u2} M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3))))) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) _inst_3)))))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] {f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) (OfNat.ofNat.{u2} M' 0 (Zero.toOfNat0.{u2} M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3))))) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_zero IsLocalizedModule.mk'_eq_zeroₓ'. -/
 @[simp]
 theorem mk'_eq_zero {m : M} (s : S) : mk' f m s = 0 ↔ f m = 0 := by rw [mk'_eq_iff, smul_zero]
@@ -1562,7 +1562,7 @@ variable (S)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M}, Iff (Eq.{succ u3} M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m) (OfNat.ofNat.{u3} M' 0 (OfNat.mk.{u3} M' 0 (Zero.zero.{u3} M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))))))) (Exists.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (fun (s' : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) => Eq.{succ u2} M (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M (Submonoid.hasSmul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_5)))) S) s' m) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M}, Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (AddMonoid.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (AddCommMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) _inst_3))))) (Exists.{succ u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (fun (s' : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) => Eq.{succ u2} M (HSMul.hSMul.{u1, u2, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M M (instHSMul.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M (Submonoid.smul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_5)))) S)) s' m) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M}, Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) (AddMonoid.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) (AddCommMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') m) _inst_3))))) (Exists.{succ u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (fun (s' : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) => Eq.{succ u2} M (HSMul.hSMul.{u1, u2, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M M (instHSMul.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M (Submonoid.smul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_5)))) S)) s' m) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.eq_zero_iff IsLocalizedModule.eq_zero_iffₓ'. -/
 theorem eq_zero_iff {m : M} : f m = 0 ↔ ∃ s' : S, s' • m = 0 :=
   (mk'_eq_zero (1 : S)).symm.trans (mk'_eq_zero' f _)
@@ -1587,7 +1587,7 @@ section Algebra
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {S' : Type.{u3}} [_inst_9 : CommRing.{u1} R] [_inst_10 : CommRing.{u2} S] [_inst_11 : CommRing.{u3} S'] [_inst_12 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10))] [_inst_13 : Algebra.{u1, u3} R S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11))] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) (f : AlgHom.{u1, u2, u3} R S S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_12 _inst_13), (forall (x : R), (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) x M) -> (IsUnit.{u3} S' (Ring.toMonoid.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R S' (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))) (fun (_x : RingHom.{u1, u3} R S' (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))) => R -> S') (RingHom.hasCoeToFun.{u1, u3} R S' (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))) (algebraMap.{u1, u3} R S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_13) x))) -> (forall (y : S'), Exists.{max (succ u2) (succ u1)} (Prod.{u2, u1} S (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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_inst_9))))))) M) (fun (m : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) M) => Eq.{succ u2} S (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) M) S (Submonoid.hasSmul.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))) (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 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))) (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 (CommRing.toCommSemiring.{u1} R _inst_9)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) _inst_12))))) M) m x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))))))) -> (IsLocalizedModule.{u1, u2, u3} R _inst_9 M S S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u1, u3} R S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_13) (AlgHom.toLinearMap.{u1, u2, u3} R S S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_12 _inst_13 f))
 but is expected to have type
-  forall {R : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_9 : CommRing.{u3} R] [_inst_10 : CommRing.{u2} S] [_inst_11 : CommRing.{u1} S'] [_inst_12 : Algebra.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))] [_inst_13 : Algebra.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (f : AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13), (forall (x : R), (Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) _inst_11)))) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))) (RingHom.instRingHomClassRingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (algebraMap.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) x))) -> (forall (y : S'), Exists.{max (succ u3) (succ u2)} (Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M))) (fun (x : Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M))) => Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') (Prod.fst.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x)) (HSMul.hSMul.{u3, u1, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S' ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') (Prod.fst.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x)) (instHSMul.{u3, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S' (Submonoid.smul.{u3, u1} R S' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (Algebra.toSMul.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) M)) (Prod.snd.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12))))) (SMulZeroClass.toSMul.{u3, u1} R S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' 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(CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12)) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R S S' (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHomClass.linearMapClass.{u3, u2, u1, max u2 u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (AlgHom.algHomClass.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13))))) f (Prod.fst.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x)))) -> (forall (x : S), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R S S' 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(CommRing.toCommSemiring.{u2} S _inst_10)))))))) -> (IsLocalizedModule.{u3, u2, u1} R _inst_9 M S S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHom.toLinearMap.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 f))
+  forall {R : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_9 : CommRing.{u3} R] [_inst_10 : CommRing.{u2} S] [_inst_11 : CommRing.{u1} S'] [_inst_12 : Algebra.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))] [_inst_13 : Algebra.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (f : AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13), (forall (x : R), (Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) _inst_11)))) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))) (RingHom.instRingHomClassRingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (algebraMap.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) x))) -> (forall (y : S'), Exists.{max (succ u3) (succ u2)} (Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M))) (fun (x : Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M))) => Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') (Prod.fst.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x)) (HSMul.hSMul.{u3, u1, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S' ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') (Prod.fst.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x)) (instHSMul.{u3, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S' (Submonoid.smul.{u3, u1} R S' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (Algebra.toSMul.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) M)) (Prod.snd.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12))))) (SMulZeroClass.toSMul.{u3, u1} R S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribMulAction.toDistribSMul.{u3, u1} R S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' 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(CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R S S' (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHomClass.linearMapClass.{u3, u2, u1, max u2 u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (AlgHom.algHomClass.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13))))) f (Prod.fst.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x)))) -> (forall (x : S), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R S S' 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(CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) 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(MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S S (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S (Submonoid.smul.{u3, u2} R S (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (Algebra.toSMul.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) M)) m x) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))))) -> (IsLocalizedModule.{u3, u2, u1} R _inst_9 M S S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHom.toLinearMap.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 f))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk_of_algebra IsLocalizedModule.mkOfAlgebraₓ'. -/
 theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [Algebra R S]
     [Algebra R S'] (M : Submonoid R) (f : S →ₐ[R] S') (h₁ : ∀ x ∈ M, IsUnit (algebraMap R S' x))

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

@@ -622,7 +622,7 @@ instance {A : Type _} [Semiring A] [Algebra R A] : Algebra (Localization S) (Loc
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {A : Type.{u2}} [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] (a : R) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S), Eq.{succ (max u1 u2)} (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (RingHom.{u1, max u1 u2} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (Localization.commSemiring.{u1} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u1 u2} (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) (LocalizedModule.semiring.{u1, u2} R _inst_1 A _inst_4 _inst_5 S))) (fun (_x : RingHom.{u1, max u1 u2} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (Localization.commSemiring.{u1} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u1 u2} (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) (LocalizedModule.semiring.{u1, u2} R _inst_1 A _inst_4 _inst_5 S))) => (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) -> (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5))) (RingHom.hasCoeToFun.{u1, max u1 u2} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (Localization.commSemiring.{u1} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u1 u2} (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) (LocalizedModule.semiring.{u1, u2} R _inst_1 A _inst_4 _inst_5 S))) (algebraMap.{u1, max u1 u2} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) (Localization.commSemiring.{u1} R _inst_1 S) (LocalizedModule.semiring.{u1, u2} R _inst_1 A _inst_4 _inst_5 S) (LocalizedModule.algebra.{u1, u2} R _inst_1 S A _inst_4 _inst_5)) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S a s)) (LocalizedModule.mk.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _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_4)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_4)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_4)) (algebraMap.{u1, u2} R A _inst_1 _inst_4 _inst_5) a) s)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {A : Type.{u1}} [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] (a : R) (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) x S)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) => LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S a s)) (FunLike.coe.{max (succ (max u2 u1)) (succ u2), succ u2, succ (max u2 u1)} (RingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S))) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (fun (_x : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) => LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S))) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toMul.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S))) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S))) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S)) (RingHom.instRingHomClassRingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S)))))) (algebraMap.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S) (LocalizedModule.instAlgebraLocalizationToCommMonoidLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleInstCommSemiringLocalizationToCommMonoidInstSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5)) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S a s)) (LocalizedModule.mk.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4))))) (algebraMap.{u2, u1} R A _inst_1 _inst_4 _inst_5) a) s)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {A : Type.{u1}} [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] (a : R) (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) x S)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) => LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S a s)) (FunLike.coe.{max (succ (max u2 u1)) (succ u2), succ u2, succ (max u2 u1)} (RingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S))) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (fun (_x : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) => LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S))) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toMul.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S))) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S))) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S)) (RingHom.instRingHomClassRingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S)))))) (algebraMap.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5 S) (LocalizedModule.instAlgebraLocalizationToCommMonoidLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleInstCommSemiringLocalizationToCommMonoidInstSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4 _inst_5)) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S a s)) (LocalizedModule.mk.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) _inst_1 _inst_4 _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4))))) (algebraMap.{u2, u1} R A _inst_1 _inst_4 _inst_5) a) s)
 Case conversion may be inaccurate. Consider using '#align localized_module.algebra_map_mk LocalizedModule.algebraMap_mkₓ'. -/
 theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
     algebraMap _ _ (Localization.mk a s) = mk (algebraMap R A a) s :=
@@ -716,7 +716,7 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S) (p : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3), Eq.{succ (max u1 u2)} (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) => (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) -> (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LocalizedModule.divBy.{u1, u2} R _inst_1 S M _inst_2 _inst_3 s) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) => (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) -> (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (RingHom.{u1, max u1 u2} R (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)))) (fun (_x : RingHom.{u1, max u1 u2} R (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)))) => R -> 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 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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_inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.instAlgebraEndToSemiringSemiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _inst_1 (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) S)) s)) p)) p
 Case conversion may be inaccurate. Consider using '#align localized_module.div_by_mul_by LocalizedModule.divBy_mul_byₓ'. -/
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
     divBy s (algebraMap R (Module.End R (LocalizedModule S M)) s p) = p :=
@@ -731,7 +731,7 @@ theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S) (p : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3), Eq.{succ (max u1 u2)} (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) => (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) -> (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (RingHom.{u1, max u1 u2} R (Module.End.{u1, max u1 u2} R 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(CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LocalizedModule.divBy.{u1, u2} R _inst_1 S M _inst_2 _inst_3 s) p)) p
 but is expected to have type
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_inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (fun (_x : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) => LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LocalizedModule.divBy.{u1, u2} R _inst_1 S M _inst_2 _inst_3 s) p)) p
 Case conversion may be inaccurate. Consider using '#align localized_module.mul_by_div_by LocalizedModule.mul_by_divByₓ'. -/
 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
     algebraMap R (Module.End R (LocalizedModule S M)) s (divBy s p) = p :=
@@ -777,7 +777,7 @@ namespace LocalizedModule
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4], (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) -> (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M''
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4], (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x)) (Module.End.monoid.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x))) -> (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M''
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4], (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x)) (Module.End.monoid.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x))) -> (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M''
 Case conversion may be inaccurate. Consider using '#align localized_module.lift' LocalizedModule.lift'ₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -817,7 +817,7 @@ noncomputable def lift' (g : M →ₗ[R] M'')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 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(NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (h s)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) => M -> M'') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) g m))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R 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_inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u1} M'' (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (LocalizedModule.mk.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u1} R R M'' M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_4 _inst_7 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Inv.inv.{u1} (Units.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (Units.instInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (IsUnit.unit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, 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(Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
 Case conversion may be inaccurate. Consider using '#align localized_module.lift'_mk LocalizedModule.lift'_mkₓ'. -/
 theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (m : M) (s : S) : LocalizedModule.lift' S g h (LocalizedModule.mk m s) = (h s).Unit⁻¹.1 (g m) :=
@@ -828,7 +828,7 @@ theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Mo
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) (x : LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (y : LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u3} M'' (LocalizedModule.lift'.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (instHAdd.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.hasAdd.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) x y)) (HAdd.hAdd.{u3, u3, u3} M'' M'' M'' (instHAdd.{u3} M'' (AddZeroClass.toHasAdd.{u3} M'' (AddMonoid.toAddZeroClass.{u3} M'' (AddCommMonoid.toAddMonoid.{u3} M'' _inst_4)))) (LocalizedModule.lift'.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h x) (LocalizedModule.lift'.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h y))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (y : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u1} M'' (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (instHAdd.{max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) x y)) (HAdd.hAdd.{u1, u1, u1} M'' M'' M'' (instHAdd.{u1} M'' (AddZeroClass.toAdd.{u1} M'' (AddMonoid.toAddZeroClass.{u1} M'' (AddCommMonoid.toAddMonoid.{u1} M'' _inst_4)))) (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h x) (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h y))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (y : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u1} M'' (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (instHAdd.{max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) x y)) (HAdd.hAdd.{u1, u1, u1} M'' M'' M'' (instHAdd.{u1} M'' (AddZeroClass.toAdd.{u1} M'' (AddMonoid.toAddZeroClass.{u1} M'' (AddCommMonoid.toAddMonoid.{u1} M'' _inst_4)))) (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h x) (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h y))
 Case conversion may be inaccurate. Consider using '#align localized_module.lift'_add LocalizedModule.lift'_addₓ'. -/
 theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (x y) :
@@ -851,7 +851,7 @@ theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 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(RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) (r : R) (m : LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u3} M'' (SMul.smul.{u1, u3} R M'' (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 (Ring.toSemiring.{u1} R (CommRing.toRing.{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 (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M'' (AddMonoid.toAddZeroClass.{u3} M'' (AddCommMonoid.toAddMonoid.{u3} M'' _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)))) r (LocalizedModule.lift'.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h m)) (LocalizedModule.lift'.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (SMul.smul.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toHasSmul.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddZeroClass.toHasZero.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5))))) r m))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (r : R) (m : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u1} M'' (HSMul.hSMul.{u3, u1, u1} R M'' M'' (instHSMul.{u3, u1} R M'' (SMulZeroClass.toSMul.{u3, u1} R M'' (AddMonoid.toZero.{u1} M'' (AddCommMonoid.toAddMonoid.{u1} M'' _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M'' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M'' (AddCommMonoid.toAddMonoid.{u1} M'' _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M'' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M'' (AddCommMonoid.toAddMonoid.{u1} M'' _inst_4)) (Module.toMulActionWithZero.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))))) r (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h m)) (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (HSMul.hSMul.{u3, max u3 u2, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (instHSMul.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toSMul.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instZeroLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulWithZero.toSMulZeroClass.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.instZeroLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MulActionWithZero.toSMulWithZero.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.instZeroLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (Module.toMulActionWithZero.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)))))) r m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (r : R) (m : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u1} M'' (HSMul.hSMul.{u3, u1, u1} R M'' M'' (instHSMul.{u3, u1} R M'' (SMulZeroClass.toSMul.{u3, u1} R M'' (AddMonoid.toZero.{u1} M'' (AddCommMonoid.toAddMonoid.{u1} M'' _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M'' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M'' (AddCommMonoid.toAddMonoid.{u1} M'' _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M'' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M'' (AddCommMonoid.toAddMonoid.{u1} M'' _inst_4)) (Module.toMulActionWithZero.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))))) r (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h m)) (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (HSMul.hSMul.{u3, max u3 u2, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (instHSMul.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toSMul.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instZeroLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulWithZero.toSMulZeroClass.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.instZeroLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MulActionWithZero.toSMulWithZero.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.instZeroLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (Module.toMulActionWithZero.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)))))) r m))
 Case conversion may be inaccurate. Consider using '#align localized_module.lift'_smul LocalizedModule.lift'_smulₓ'. -/
 theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (r : R) (m) : r • LocalizedModule.lift' S g h m = LocalizedModule.lift' S g h (r • m) :=
@@ -867,7 +867,7 @@ theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4], (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) -> (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4], (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x)) (Module.End.monoid.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x))) -> (LinearMap.{u1, u1, max u2 u1, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4], (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x)) (Module.End.monoid.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x))) -> (LinearMap.{u1, u1, max u2 u1, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7)
 Case conversion may be inaccurate. Consider using '#align localized_module.lift LocalizedModule.liftₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -885,7 +885,7 @@ noncomputable def lift (g : M →ₗ[R] M'')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) (m : M) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M'' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M'') (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R 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=> M'' -> M'') (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M'' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_4 _inst_7 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Units.val.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Inv.inv.{u3} (Units.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (Units.hasInv.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (IsUnit.unit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R 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(NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (h s)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) => M -> M'') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) g m))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, 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_inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M'') (LocalizedModule.mk.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LocalizedModule.lift.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) (LocalizedModule.mk.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u1} R R M'' M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_4 _inst_7 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Inv.inv.{u1} (Units.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (Units.instInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (IsUnit.unit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
 Case conversion may be inaccurate. Consider using '#align localized_module.lift_mk LocalizedModule.lift_mkₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -900,7 +900,7 @@ theorem lift_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Mod
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))), Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u1, u1, u1, u2, max u1 u2, u3} R R R M (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 _inst_5 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LocalizedModule.lift.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) (LocalizedModule.mkLinearMap.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) g
 but is expected to have type
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(x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} 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_inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, 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(Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))), Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u3, u3, u3, u2, max u3 u2, u1} R R R M (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 _inst_5 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomCompTriple.ids.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LocalizedModule.lift.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) (LocalizedModule.mkLinearMap.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) g
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))), Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u3, u3, u3, u2, max u3 u2, u1} R R R M (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 _inst_5 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomCompTriple.ids.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LocalizedModule.lift.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) (LocalizedModule.mkLinearMap.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) g
 Case conversion may be inaccurate. Consider using '#align localized_module.lift_comp LocalizedModule.lift_compₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -917,7 +917,7 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) (l : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7), (Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u1, u1, u1, u2, max u1 u2, u3} R R R M (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 _inst_5 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) l (LocalizedModule.mkLinearMap.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) g) -> (Eq.{max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7) (LocalizedModule.lift.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) l)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (l : LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7), (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u3, u3, u3, u2, max u3 u2, u1} R R R M (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 _inst_5 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomCompTriple.ids.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) l (LocalizedModule.mkLinearMap.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) g) -> (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7) (LocalizedModule.lift.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) l)
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (l : LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7), (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u3, u3, u3, u2, max u3 u2, u1} R R R M (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 _inst_5 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomCompTriple.ids.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) l (LocalizedModule.mkLinearMap.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) g) -> (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7) (LocalizedModule.lift.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) l)
 Case conversion may be inaccurate. Consider using '#align localized_module.lift_unique LocalizedModule.lift_uniqueₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible and
@@ -990,7 +990,7 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M' _inst_3 _inst_3 _inst_6 _inst_6) => M' -> M') (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M' M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeBaseAux.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Units.hasCoe.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) (Inv.inv.{u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Units.hasInv.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) => R -> (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.algebra.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_3 _inst_6)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R 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LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m))
 but is expected to have type
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_inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.fromLocalizedModule'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (LocalizedModule.mk.{u3, u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' 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(Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.fromLocalizedModule'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M' (fun (x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M') => M') x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M' M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Inv.inv.{u2} (Units.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (Units.instInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_mk IsLocalizedModule.fromLocalizedModule'_mkₓ'. -/
 @[simp]
 theorem fromLocalizedModule'_mk (m : M) (s : S) :
@@ -1061,7 +1061,7 @@ noncomputable def fromLocalizedModule : LocalizedModule S M →ₗ[R] M'
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ 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_inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (fun (x : Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) => M' -> M') (coeFnTrans.{succ u3, succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M' _inst_3 _inst_3 _inst_6 _inst_6) => M' -> M') (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M' M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeBaseAux.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Units.hasCoe.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) (Inv.inv.{u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Units.hasInv.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) => R -> (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.algebra.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_3 _inst_6)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (IsLocalizedModule.map_units.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R 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(CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), succ u2} (LinearMap.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M' (fun (x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M') => M') x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M' M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Inv.inv.{u2} (Units.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (Units.instInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module_mk IsLocalizedModule.fromLocalizedModule_mkₓ'. -/
 theorem fromLocalizedModule_mk (m : M) (s : S) :
     fromLocalizedModule S f (LocalizedModule.mk m s) =
@@ -1131,7 +1131,7 @@ noncomputable def iso : LocalizedModule S M ≃ₗ[R] M' :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearEquiv.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearEquiv.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1)) (IsLocalizedModule.iso.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8) (LocalizedModule.mk.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5 m s)) (coeFn.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (fun (x : Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) => M' -> M') (coeFnTrans.{succ u3, succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M' _inst_3 _inst_3 _inst_6 _inst_6) => M' -> M') (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M' M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeBaseAux.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Units.hasCoe.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) (Inv.inv.{u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Units.hasInv.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) => R -> (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.algebra.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_3 _inst_6)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (IsLocalizedModule.map_units.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), succ u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R 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(CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (SMulZeroClass.toSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R 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(CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (SemilinearMapClass.distribMulActionHomClass.{u3, max u3 u1, u2, max (max u3 u1) u2} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) 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(CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (IsLocalizedModule.iso.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M' (fun (x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M') => M') x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M' M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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(MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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_inst_1)) _inst_3 _inst_6) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), succ u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u3, max u3 u1, u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (SMulZeroClass.toSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) 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(Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_apply_mk IsLocalizedModule.iso_apply_mkₓ'. -/
 theorem iso_apply_mk (m : M) (s : S) :
     iso S f (LocalizedModule.mk m s) = (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
@@ -1187,7 +1187,7 @@ theorem iso_symm_comp : (iso S f).symm.toLinearMap.comp f = LocalizedModule.mkLi
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} {M'' : Type.{u4}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_4 : AddCommMonoid.{u4} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] [_inst_7 : Module.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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_inst_4 _inst_7))) (algebraMap.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u4} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) -> (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} {M'' : Type.{u4}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_4 : AddCommMonoid.{u4} M''] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] [_inst_7 : Module.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), IsUnit.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x)) (Module.End.monoid.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u1, u4} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x))) -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} {M'' : Type.{u4}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_4 : AddCommMonoid.{u4} M''] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] [_inst_7 : Module.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), IsUnit.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x)) (Module.End.monoid.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u1, u4} R (Module.End.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u4} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u1, u4} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x))) -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7)
 Case conversion may be inaccurate. Consider using '#align is_localized_module.lift IsLocalizedModule.liftₓ'. -/
 /--
 If `M'` is a localized module and `g` is a linear map `M' → M''` such that all scalar multiplication
@@ -1202,7 +1202,7 @@ noncomputable def lift (g : M →ₗ[R] M'')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} {M'' : Type.{u4}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_4 : AddCommMonoid.{u4} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] [_inst_7 : Module.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u4} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))), Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M M' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.lift.{u1, u2, u3, u4} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) f) g
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u3}} {M' : Type.{u1}} {M'' : Type.{u2}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_4 : AddCommMonoid.{u2} M''] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u1} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u2} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))), Eq.{max (succ u3) (succ u2)} (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u3, u1, u2} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (IsLocalizedModule.lift.{u4, u3, u1, u2} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) f) g
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u3}} {M' : Type.{u1}} {M'' : Type.{u2}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_4 : AddCommMonoid.{u2} M''] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u1} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u2} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))), Eq.{max (succ u3) (succ u2)} (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u3, u1, u2} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (IsLocalizedModule.lift.{u4, u3, u1, u2} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) f) g
 Case conversion may be inaccurate. Consider using '#align is_localized_module.lift_comp IsLocalizedModule.lift_compₓ'. -/
 theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x)) :
     (lift S f g h).comp f = g :=
@@ -1217,7 +1217,7 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} {M'' : Type.{u4}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_4 : AddCommMonoid.{u4} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] [_inst_7 : Module.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R 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_inst_4 _inst_7))) (algebraMap.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u4} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) (l : LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7), (Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M M' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) l f) g) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) (IsLocalizedModule.lift.{u1, u2, u3, u4} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) l)
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u3}} {M' : Type.{u1}} {M'' : Type.{u2}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_4 : AddCommMonoid.{u2} M''] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u1} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u2} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))) (l : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7), (Eq.{max (succ u3) (succ u2)} (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u3, u1, u2} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) l f) g) -> (Eq.{max (succ u1) (succ u2)} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) (IsLocalizedModule.lift.{u4, u3, u1, u2} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) l)
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u3}} {M' : Type.{u1}} {M'' : Type.{u2}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_4 : AddCommMonoid.{u2} M''] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u1} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u2} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))) (l : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7), (Eq.{max (succ u3) (succ u2)} (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u3, u1, u2} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) l f) g) -> (Eq.{max (succ u1) (succ u2)} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) (IsLocalizedModule.lift.{u4, u3, u1, u2} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) l)
 Case conversion may be inaccurate. Consider using '#align is_localized_module.lift_unique IsLocalizedModule.lift_uniqueₓ'. -/
 theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (l : M' →ₗ[R] M'') (hl : l.comp f = g) : lift S f g h = l :=
@@ -1237,7 +1237,7 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} {M'' : Type.{u4}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_4 : AddCommMonoid.{u4} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] [_inst_7 : Module.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7), (forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u4} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R 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(Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) -> (ExistsUnique.{max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) (fun (l : LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) => Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M M' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) l f) g))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u3}} {M' : Type.{u1}} {M'' : Type.{u2}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_4 : AddCommMonoid.{u2} M''] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u1} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7), (forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => 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(Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u2} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))) -> (ExistsUnique.{max (succ u1) (succ u2)} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) (fun (l : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) => Eq.{max (succ u3) (succ u2)} (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u3, u1, u2} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) l f) g))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u3}} {M' : Type.{u1}} {M'' : Type.{u2}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_4 : AddCommMonoid.{u2} M''] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u1} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7), (forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => 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(CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u2} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))) -> (ExistsUnique.{max (succ u1) (succ u2)} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) (fun (l : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) => Eq.{max (succ u3) (succ u2)} (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u3, u1, u2} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) l f) g))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.is_universal IsLocalizedModule.is_universalₓ'. -/
 /-- Universal property from localized module:
 If `(M', f : M ⟶ M')` is a localized module then it satisfies the following universal property:
@@ -1263,7 +1263,7 @@ theorem is_universal :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} {M'' : Type.{u4}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_4 : AddCommMonoid.{u4} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] [_inst_7 : Module.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], (forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u4} R (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u4} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) -> (forall {{j : LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}} {{k : LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}}, (Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M M' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) j f) (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M M' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) k f)) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) j k))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u2} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], (forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))) -> (forall {{j : LinearMap.{u4, u4, u2, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}} {{k : LinearMap.{u4, u4, u2, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}}, (Eq.{max (succ u1) (succ u3)} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u1, u2, u3} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) j f) (LinearMap.comp.{u4, u4, u4, u1, u2, u3} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) k f)) -> (Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) j k))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u2} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], (forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u3} R (Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))) -> (forall {{j : LinearMap.{u4, u4, u2, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}} {{k : LinearMap.{u4, u4, u2, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}}, (Eq.{max (succ u1) (succ u3)} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u1, u2, u3} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) j f) (LinearMap.comp.{u4, u4, u4, u1, u2, u3} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) k f)) -> (Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) j k))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.ring_hom_ext IsLocalizedModule.ringHom_extₓ'. -/
 theorem ringHom_ext (map_unit : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     ⦃j k : M' →ₗ[R] M''⦄ (h : j.comp f = k.comp f) : j = k :=
@@ -1587,7 +1587,7 @@ section Algebra
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {S' : Type.{u3}} [_inst_9 : CommRing.{u1} R] [_inst_10 : CommRing.{u2} S] [_inst_11 : CommRing.{u3} S'] [_inst_12 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10))] [_inst_13 : Algebra.{u1, u3} R S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11))] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) (f : AlgHom.{u1, u2, u3} R S S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_12 _inst_13), (forall (x : R), (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) x M) -> (IsUnit.{u3} S' (Ring.toMonoid.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R S' (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))) (fun (_x : RingHom.{u1, u3} R S' (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))) => R -> S') (RingHom.hasCoeToFun.{u1, u3} R S' (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))) (algebraMap.{u1, u3} R S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_13) x))) -> (forall (y : S'), Exists.{max (succ u2) (succ u1)} (Prod.{u2, u1} S (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) M)) (fun (x : Prod.{u2, u1} S (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) M)) => Eq.{succ u3} S' (SMul.smul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) M) S' (Submonoid.hasSmul.{u1, u3} R S' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u3} R S' (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R S' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9)))))) (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R S' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))))))) (Module.toMulActionWithZero.{u1, u3} R S' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11))))) (Algebra.toModule.{u1, u3} R S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_13))))) M) (Prod.snd.{u2, u1} 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AlgHom.{u1, u2, u3} R S S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_12 _inst_13) => S -> S') ([anonymous].{u1, u2, u3} R S S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_12 _inst_13) f (Prod.fst.{u2, u1} S (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R 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(Zero.zero.{u3} S' (MulZeroClass.toHasZero.{u3} S' (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S' (NonAssocRing.toNonUnitalNonAssocRing.{u3} S' (Ring.toNonAssocRing.{u3} S' (CommRing.toRing.{u3} S' _inst_11)))))))))) -> (Exists.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) M) (fun (m : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) M) => Eq.{succ u2} S (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) M) S (Submonoid.hasSmul.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))) (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 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))) (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 (CommRing.toCommSemiring.{u1} R _inst_9)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) _inst_12))))) M) m x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))))))) -> (IsLocalizedModule.{u1, u2, u3} R _inst_9 M S S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u1, u3} R S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_13) (AlgHom.toLinearMap.{u1, u2, u3} R S S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_12 _inst_13 f))
 but is expected to have type
-  forall {R : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_9 : CommRing.{u3} R] [_inst_10 : CommRing.{u2} S] [_inst_11 : CommRing.{u1} S'] [_inst_12 : Algebra.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))] [_inst_13 : Algebra.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (f : AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13), (forall (x : R), (Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) _inst_11)))) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))) (RingHom.instRingHomClassRingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (algebraMap.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) x))) -> (forall (y : S'), Exists.{max (succ u3) (succ u2)} (Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M))) (fun (x : Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12))))) (SMulZeroClass.toSMul.{u3, u1} R S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribMulAction.toDistribSMul.{u3, u1} R S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12)) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R S S' (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHomClass.linearMapClass.{u3, u2, u1, max u2 u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (AlgHom.algHomClass.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13))))) f x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) _inst_11)))))) -> (Exists.{succ u3} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) (fun (m : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) => Eq.{succ u2} S (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S S (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S (Submonoid.smul.{u3, u2} R S (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (Algebra.toSMul.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) M)) m x) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))))) -> (IsLocalizedModule.{u3, u2, u1} R _inst_9 M S S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHom.toLinearMap.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 f))
+  forall {R : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_9 : CommRing.{u3} R] [_inst_10 : CommRing.{u2} S] [_inst_11 : CommRing.{u1} S'] [_inst_12 : Algebra.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))] [_inst_13 : Algebra.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (f : AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13), (forall (x : R), (Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') x) _inst_11)))) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S') _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))) (RingHom.instRingHomClassRingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (algebraMap.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) x))) -> (forall (y : S'), Exists.{max (succ u3) (succ u2)} (Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M))) (fun (x : Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (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 (CommRing.toCommSemiring.{u2} S _inst_10))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R S (AddMonoid.toAddZeroClass.{u2} S 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(CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12))))) (SMulZeroClass.toSMul.{u3, u1} R S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribMulAction.toDistribSMul.{u3, u1} R S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12)) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R S S' (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHomClass.linearMapClass.{u3, u2, u1, max u2 u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (AlgHom.algHomClass.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13))))) f x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) _inst_11)))))) -> (Exists.{succ u3} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) (fun (m : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) => Eq.{succ u2} S (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S S (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S (Submonoid.smul.{u3, u2} R S (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (Algebra.toSMul.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) M)) m x) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))))) -> (IsLocalizedModule.{u3, u2, u1} R _inst_9 M S S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHom.toLinearMap.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 f))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk_of_algebra IsLocalizedModule.mkOfAlgebraₓ'. -/
 theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [Algebra R S]
     [Algebra R S'] (M : Submonoid R) (f : S →ₐ[R] S') (h₁ : ∀ x ∈ M, IsUnit (algebraMap R S' x))

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang, Jujian Zhang
 
 ! This file was ported from Lean 3 source module algebra.module.localized_module
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
+! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Algebra.Algebra.RestrictScalars
 /-!
 # Localized Module
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a commutative ring `R`, a multiplicative subset `S ⊆ R` and an `R`-module `M`, we can localize
 `M` by `S`. This gives us a `localization S`-module.
 
@@ -713,7 +716,7 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S) (p : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3), Eq.{succ (max u1 u2)} (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))))))) (algebraMap.{u1, max u2 u1} R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) _inst_1 (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.instAlgebraEndToSemiringSemiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _inst_1 (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) S)) s)) p)) p
 Case conversion may be inaccurate. Consider using '#align localized_module.div_by_mul_by LocalizedModule.divBy_mul_byₓ'. -/
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
     divBy s (algebraMap R (Module.End R (LocalizedModule S M)) s p) = p :=
@@ -728,7 +731,7 @@ theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S) (p : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3), Eq.{succ (max u1 u2)} (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) => (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) -> (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (RingHom.{u1, max u1 u2} R (Module.End.{u1, max u1 u2} R 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_inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))) (RingHom.hasCoeToFun.{u1, max u1 u2} R (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (Module.End.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
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(LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (RingHom.{u1, max u2 u1} R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)))) R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{max u2 u1} (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, max u1 u2} (RingHom.{u1, max u2 u1} R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)))) R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))))))) (algebraMap.{u1, max u2 u1} R (Module.End.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) _inst_1 (Module.End.semiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (Module.instAlgebraEndToSemiringSemiring.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _inst_1 (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (fun (_x : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) => LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LocalizedModule.divBy.{u1, u2} R _inst_1 S M _inst_2 _inst_3 s) p)) p
 Case conversion may be inaccurate. Consider using '#align localized_module.mul_by_div_by LocalizedModule.mul_by_divByₓ'. -/
 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
     algebraMap R (Module.End R (LocalizedModule S M)) s (divBy s p) = p :=
@@ -814,7 +817,7 @@ noncomputable def lift' (g : M →ₗ[R] M'')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} 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_inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) g m))
 but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u1} M'' (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (LocalizedModule.mk.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u1} R R M'' M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_4 _inst_7 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Inv.inv.{u1} (Units.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (Units.instInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (IsUnit.unit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
 Case conversion may be inaccurate. Consider using '#align localized_module.lift'_mk LocalizedModule.lift'_mkₓ'. -/
 theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (m : M) (s : S) : LocalizedModule.lift' S g h (LocalizedModule.mk m s) = (h s).Unit⁻¹.1 (g m) :=
@@ -882,7 +885,7 @@ noncomputable def lift (g : M →ₗ[R] M'')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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(Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (h s)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) => M -> M'') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) g m))
 but is expected to have type
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_inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, 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(Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M'') (LocalizedModule.mk.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LocalizedModule.lift.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) (LocalizedModule.mk.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M'' (fun (_x : M'') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M'') => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u1} R R M'' M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_4 _inst_7 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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(CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (Units.instInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (IsUnit.unit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R 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_inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (h s)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M'') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g m))
 Case conversion may be inaccurate. Consider using '#align localized_module.lift_mk LocalizedModule.lift_mkₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
@@ -987,7 +990,7 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M' _inst_3 _inst_3 _inst_6 _inst_6) => M' -> M') (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M' M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeBaseAux.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Units.hasCoe.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) (Inv.inv.{u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Units.hasInv.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m))
 but is expected to have type
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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.fromLocalizedModule'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M' (fun (x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M') => M') x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M' M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Inv.inv.{u2} (Units.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (Units.instInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_mk IsLocalizedModule.fromLocalizedModule'_mkₓ'. -/
 @[simp]
 theorem fromLocalizedModule'_mk (m : M) (s : S) :
@@ -1058,7 +1061,7 @@ noncomputable def fromLocalizedModule : LocalizedModule S M →ₗ[R] M'
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m))
 but is expected to have type
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_inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') 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(NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Inv.inv.{u2} (Units.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') 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_inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, u2} R R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8) (LocalizedModule.mk.{u3, 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(LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M' M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Inv.inv.{u2} (Units.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) 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(CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))) R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module_mk IsLocalizedModule.fromLocalizedModule_mkₓ'. -/
 theorem fromLocalizedModule_mk (m : M) (s : S) :
     fromLocalizedModule S f (LocalizedModule.mk m s) =
@@ -1070,7 +1073,7 @@ theorem fromLocalizedModule_mk (m : M) (s : S) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Injective.{succ (max u1 u2), succ u3} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Injective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Injective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.injₓ'. -/
 theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f := fun x y eq1 =>
   by
@@ -1088,7 +1091,7 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Surjective.{succ (max u1 u2), succ u3} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Surjective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Surjective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.surj IsLocalizedModule.fromLocalizedModule.surjₓ'. -/
 theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S f := fun x =>
   let ⟨⟨m, s⟩, eq1⟩ := IsLocalizedModule.surj S f x
@@ -1102,7 +1105,7 @@ theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Bijective.{succ (max u1 u2), succ u3} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Bijective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Bijective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.bij IsLocalizedModule.fromLocalizedModule.bijₓ'. -/
 theorem fromLocalizedModule.bij : Function.Bijective <| fromLocalizedModule S f :=
   ⟨fromLocalizedModule.inj _ _, fromLocalizedModule.surj _ _⟩
@@ -1128,7 +1131,7 @@ noncomputable def iso : LocalizedModule S M ≃ₗ[R] M' :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearEquiv.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearEquiv.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1)) (IsLocalizedModule.iso.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8) (LocalizedModule.mk.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5 m s)) (coeFn.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (fun (x : Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) => M' -> M') (coeFnTrans.{succ u3, succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u1, u3, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M' _inst_3 _inst_3 _inst_6 _inst_6) => M' -> M') (LinearMap.hasCoeToFun.{u1, u1, u3, u3} R R M' M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeBaseAux.{succ u3, succ u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Units.hasCoe.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) (Inv.inv.{u3} (Units.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (Units.hasInv.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.monoid.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) => R -> (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6) (Module.End.algebra.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_3 _inst_6)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (IsLocalizedModule.map_units.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') 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(CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (SMulZeroClass.toSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M' (AddMonoid.toAddZeroClass.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u3, max u3 u1, u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R 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M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u1), succ u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u3, max u3 u1, u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (SMulZeroClass.toSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M' (AddMonoid.toAddZeroClass.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u3, max u3 u1, u2} (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (SemilinearMapClass.distribMulActionHomClass.{u3, max u3 u1, u2, max (max u3 u1) u2} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, max u3 u1, u2, max (max u3 u1) u2} R R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LinearEquiv.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, max u3 u1, u2} R R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (IsLocalizedModule.iso.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) M' (fun (x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M') => M') x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M' M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_3 _inst_6 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Units.val.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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(CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (Units.instInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (Module.End.monoid.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)) (IsUnit.unit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) 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(Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))))) (algebraMap.{u3, u2} R (Module.End.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_3 _inst_6)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) s)) (IsLocalizedModule.map_units.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 s)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_apply_mk IsLocalizedModule.iso_apply_mkₓ'. -/
 theorem iso_apply_mk (m : M) (s : S) :
     iso S f (LocalizedModule.mk m s) = (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
@@ -1139,7 +1142,7 @@ theorem iso_apply_mk (m : M) (s : S) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M'), Eq.{succ (max u1 u2)} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (LinearEquiv.{u1, u1, u3, max u1 u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) (fun (_x : LinearEquiv.{u1, u1, u3, 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(IsLocalizedModule.surj.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M'), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M') => LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) m) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearEquiv.{u3, u3, u1, max u3 u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M') => LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u3, u1, max u3 u2} (LinearEquiv.{u3, u3, u1, max u3 u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toSMul.{u3, u1} R M' (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u1} R M' (AddMonoid.toAddZeroClass.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (DistribMulAction.toDistribSMul.{u3, u1} R M' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} M' _inst_3) (Module.toDistribMulAction.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribMulAction.toDistribSMul.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u3, u1, max u3 u2} (LinearEquiv.{u3, u3, u1, max u3 u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) 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+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R 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R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) (Prod.snd.{u2, u3} M (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) x) m) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f (Prod.fst.{u2, u3} M (Subtype.{succ u3} R (fun (x : R) => 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f (Prod.fst.{u2, u3} M (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) x))) (IsLocalizedModule.surj.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m))))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_apply_aux IsLocalizedModule.iso_symm_apply_auxₓ'. -/
 theorem iso_symm_apply_aux (m : M') :
     (iso S f).symm m =
@@ -1157,7 +1160,7 @@ theorem iso_symm_apply_aux (m : M') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M') (a : M) (b : coeSort.{succ u1, 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u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (Submonoid.hasSmul.{u1, u3} R M' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) (fun (_x : LinearEquiv.{u1, u1, u3, max u1 u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) => M' -> (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max u1 u2} R R M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8)) m) (LocalizedModule.mk.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5 a b))
 but is expected to have type
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_inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M') (a : M) (b : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), (Eq.{succ u2} M' (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R 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(MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) b m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M') => LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u3, u2, max u3 u1} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (DistribSMul.toSMulZeroClass.{u3, u2} R M' (AddMonoid.toAddZeroClass.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u3, u2, max u3 u1} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, max u3 u1, max (max u3 u1) u2} R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, max u3 u1, max (max u3 u1) u2} R R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, max u3 u1} R R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearEquiv.symm.{u3, u3, max u3 u1, u2} R R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IsLocalizedModule.iso.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8)) m) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 a b))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M') (a : M) (b : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), (Eq.{succ u2} M' (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) b m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f a)) -> (Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M') => LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) m) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u2, max (succ u3) (succ u1)} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) 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(DistribSMul.toSMulZeroClass.{u3, u2} R M' (AddMonoid.toAddZeroClass.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (DistribMulAction.toDistribSMul.{u3, u2} R M' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toZero.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u3, u2, max u3 u1} (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6) (Module.toDistribMulAction.{u3, max u3 u1} R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, max u3 u1, max (max u3 u1) u2} R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, max u3 u1, max (max u3 u1) u2} R R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LinearEquiv.{u3, u3, u2, max u3 u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, max u3 u1} R R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearEquiv.symm.{u3, u3, max u3 u1, u2} R R (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IsLocalizedModule.iso.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8)) m) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 a b))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'ₓ'. -/
 theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
     (iso S f).symm m = LocalizedModule.mk a b :=
@@ -1352,7 +1355,7 @@ variable (S)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M), Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) S))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2] [_inst_6 : Module.{u2, u3} R M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3] (f : LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u2, u1, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M), Eq.{succ u3} M' (IsLocalizedModule.mk'.{u2, u1, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m (OfNat.ofNat.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) 1 (One.toOfNat1.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) (Submonoid.one.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) S)))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R M M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f m)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2] [_inst_6 : Module.{u2, u3} R M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3] (f : LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u2, u1, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M), Eq.{succ u3} M' (IsLocalizedModule.mk'.{u2, u1, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m (OfNat.ofNat.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) 1 (One.toOfNat1.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) (Submonoid.one.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) S)))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R M M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f m)
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_one IsLocalizedModule.mk'_oneₓ'. -/
 @[simp]
 theorem mk'_one (m : M) : mk' f m (1 : S) = f m :=
@@ -1368,7 +1371,7 @@ variable {S}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M (Submonoid.hasSmul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_5)))) S) s m) s) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (HSMul.hSMul.{u3, u1, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M M (instHSMul.{u3, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M (Submonoid.smul.{u3, u1} R M (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_5)))) S)) s m) s) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m)
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (HSMul.hSMul.{u3, u1, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M M (instHSMul.{u3, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M (Submonoid.smul.{u3, u1} R M (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_5)))) S)) s m) s) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m)
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancelₓ'. -/
 @[simp]
 theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m :=
@@ -1382,7 +1385,7 @@ theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (SMul.smul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (Submonoid.hasSmul.{u1, u3} R M' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) S) s (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) s (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m)
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u2} M' (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) s (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m)
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel' IsLocalizedModule.mk'_cancel'ₓ'. -/
 @[simp]
 theorem mk'_cancel' (m : M) (s : S) : s • mk' f m s = f m := by
@@ -1480,7 +1483,7 @@ theorem mk'_sub_mk' {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_9 : Semiring.{u2} M] [_inst_10 : Semiring.{u3} M'] [_inst_11 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9)))] [_inst_12 : Algebra.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)), (forall (m₁ : M) (m₂ : M), Eq.{succ u3} M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f (HMul.hMul.{u2, u2, u2} M M M (instHMul.{u2} M (Distrib.toHasMul.{u2} M (NonUnitalNonAssocSemiring.toDistrib.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))))) m₁ m₂)) (HMul.hMul.{u3, u3, u3} M' M' M' (instHMul.{u3} M' (Distrib.toHasMul.{u3} M' (NonUnitalNonAssocSemiring.toDistrib.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))))) (coeFn.{max 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m₁) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m₂))) -> (forall [_inst_13 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f] (m₁ : M) (m₂ : M) (s₁ : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (s₂ : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (HMul.hMul.{u3, u3, u3} M' M' M' (instHMul.{u3} M' (Distrib.toHasMul.{u3} M' (NonUnitalNonAssocSemiring.toDistrib.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))))) (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₁ s₁) (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₂ s₂)) (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M' (Semiring.toNonAssocSemiring.{u3} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 (HMul.hMul.{u2, u2, u2} M M M (instHMul.{u2} M (Distrib.toHasMul.{u2} M (NonUnitalNonAssocSemiring.toDistrib.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9))))) m₁ m₂) (HMul.hMul.{u1, u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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(NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (instHMul.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (Submonoid.mul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) S)) s₁ s₂)))
 but is expected to have type
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(CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)), (forall (m₁ : M) (m₂ : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m₁) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m₂) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m₁) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m₁) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 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(CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m₁) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m₂))) -> (forall [_inst_13 : IsLocalizedModule.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f] (m₁ : M) (m₂ : M) (s₁ : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (s₂ : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), Eq.{succ u2} M' (HMul.hMul.{u2, u2, u2} M' M' M' (instHMul.{u2} M' (NonUnitalNonAssocSemiring.toMul.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10)))) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₁ s₁) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₂ s₂)) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂) (HMul.hMul.{u1, u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (instHMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (Submonoid.mul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) S)) s₁ s₂)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {M : Type.{u3}} {M' : Type.{u2}} [_inst_9 : Semiring.{u3} M] [_inst_10 : Semiring.{u2} M'] [_inst_11 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))] [_inst_12 : Algebra.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)), (forall (m₁ : M) (m₂ : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m₂))) -> (forall [_inst_13 : IsLocalizedModule.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f] (m₁ : M) (m₂ : M) (s₁ : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (s₂ : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), Eq.{succ u2} M' (HMul.hMul.{u2, u2, u2} M' M' M' (instHMul.{u2} M' (NonUnitalNonAssocSemiring.toMul.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10)))) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₁ s₁) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 m₂ s₂)) (IsLocalizedModule.mk'.{u1, u3, u2} R _inst_1 S M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M' (Semiring.toNonAssocSemiring.{u2} M' _inst_10))) _inst_11 (Algebra.toModule.{u1, u2} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10 _inst_12) f _inst_13 (HMul.hMul.{u3, u3, u3} M M M (instHMul.{u3} M (NonUnitalNonAssocSemiring.toMul.{u3} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} M (Semiring.toNonAssocSemiring.{u3} M _inst_9)))) m₁ m₂) (HMul.hMul.{u1, u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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_inst_1))))))) x S)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (instHMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (Submonoid.mul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) S)) s₁ s₂)))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_mul_mk'_of_map_mul IsLocalizedModule.mk'_mul_mk'_of_map_mulₓ'. -/
 theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Module R M]
     [Algebra R M'] (f : M →ₗ[R] M') (hf : ∀ m₁ m₂, f (m₁ * m₂) = f m₁ * f m₂)
@@ -1512,7 +1515,7 @@ variable {f}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] {f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} {s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S} {m' : M'}, Iff (Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) m') (Eq.{succ u3} M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m) (SMul.smul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (Submonoid.hasSmul.{u1, u3} R M' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) S) s m'))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] {f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} {s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)} {m' : M'}, Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) m') (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m) (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) s m'))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] {f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} {s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)} {m' : M'}, Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) m') (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m) (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' M' (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) s m'))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_iff IsLocalizedModule.mk'_eq_iffₓ'. -/
 @[simp]
 theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m' := by
@@ -1523,7 +1526,7 @@ theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m'
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] {f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Iff (Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) (OfNat.ofNat.{u3} M' 0 (OfNat.mk.{u3} M' 0 (Zero.zero.{u3} M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))))))) (Eq.{succ u3} M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m) (OfNat.ofNat.{u3} M' 0 (OfNat.mk.{u3} M' 0 (Zero.zero.{u3} M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3)))))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] {f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) (OfNat.ofNat.{u2} M' 0 (Zero.toOfNat0.{u2} M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3))))) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) _inst_3)))))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] {f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6} [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) (OfNat.ofNat.{u2} M' 0 (Zero.toOfNat0.{u2} M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3))))) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_zero IsLocalizedModule.mk'_eq_zeroₓ'. -/
 @[simp]
 theorem mk'_eq_zero {m : M} (s : S) : mk' f m s = 0 ↔ f m = 0 := by rw [mk'_eq_iff, smul_zero]
@@ -1559,7 +1562,7 @@ variable (S)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M}, Iff (Eq.{succ u3} M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f m) (OfNat.ofNat.{u3} M' 0 (OfNat.mk.{u3} M' 0 (Zero.zero.{u3} M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))))))) (Exists.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (fun (s' : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) => Eq.{succ u2} M (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M (Submonoid.hasSmul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_5)))) S) s' m) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M}, Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (AddMonoid.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (AddCommMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) _inst_3))))) (Exists.{succ u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (fun (s' : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) => Eq.{succ u2} M (HSMul.hSMul.{u1, u2, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M M (instHSMul.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M (Submonoid.smul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_5)))) S)) s' m) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M}, Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (AddMonoid.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) (AddCommMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') m) _inst_3))))) (Exists.{succ u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (fun (s' : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) => Eq.{succ u2} M (HSMul.hSMul.{u1, u2, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M M (instHSMul.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M (Submonoid.smul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_5)))) S)) s' m) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align is_localized_module.eq_zero_iff IsLocalizedModule.eq_zero_iffₓ'. -/
 theorem eq_zero_iff {m : M} : f m = 0 ↔ ∃ s' : S, s' • m = 0 :=
   (mk'_eq_zero (1 : S)).symm.trans (mk'_eq_zero' f _)

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -49,13 +49,25 @@ variable {R : Type u} [CommSemiring R] (S : Submonoid R)
 
 variable (M : Type v) [AddCommMonoid M] [Module R M]
 
+/- warning: localized_module.r -> LocalizedModule.r is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (M : Type.{u2}) [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2], (Prod.{u2, u1} M (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S)) -> (Prod.{u2, u1} M (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S)) -> Prop
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (M : Type.{u2}) [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2], (Prod.{u2, u1} M (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x S))) -> (Prod.{u2, u1} M (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x S))) -> Prop
+Case conversion may be inaccurate. Consider using '#align localized_module.r LocalizedModule.rₓ'. -/
 /-- The equivalence relation on `M × S` where `(m1, s1) ≈ (m2, s2)` if and only if
 for some (u : S), u * (s2 • m1 - s1 • m2) = 0-/
-def R (a b : M × S) : Prop :=
+def r (a b : M × S) : Prop :=
   ∃ u : S, u • b.2 • a.1 = u • a.2 • b.1
-#align localized_module.r LocalizedModule.R
-
-theorem R.isEquiv : IsEquiv _ (R S M) :=
+#align localized_module.r LocalizedModule.r
+
+/- warning: localized_module.r.is_equiv -> LocalizedModule.r.isEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (M : Type.{u2}) [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2], IsEquiv.{max u2 u1} (Prod.{u2, u1} M (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S)) (LocalizedModule.r.{u1, u2} R _inst_1 S M _inst_2 _inst_3)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align localized_module.r.is_equiv LocalizedModule.r.isEquivₓ'. -/
+theorem r.isEquiv : IsEquiv _ (r S M) :=
   { refl := fun ⟨m, s⟩ => ⟨1, by rw [one_smul]⟩
     trans := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨m3, s3⟩ ⟨u1, hu1⟩ ⟨u2, hu2⟩ =>
       by
@@ -66,39 +78,65 @@ theorem R.isEquiv : IsEquiv _ (R S M) :=
       simp only [← mul_smul, smul_assoc, mul_assoc, mul_comm, mul_left_comm] at hu1' hu2'⊢
       rw [hu2', hu1']
     symm := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => ⟨u, hu.symm⟩ }
-#align localized_module.r.is_equiv LocalizedModule.R.isEquiv
-
-instance R.setoid : Setoid (M × S) where
-  R := R S M
-  iseqv := ⟨(R.isEquiv S M).refl, (R.isEquiv S M).symm, (R.isEquiv S M).trans⟩
-#align localized_module.r.setoid LocalizedModule.R.setoid
+#align localized_module.r.is_equiv LocalizedModule.r.isEquiv
+
+/- warning: localized_module.r.setoid -> LocalizedModule.r.setoid is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align localized_module.r.setoid LocalizedModule.r.setoidₓ'. -/
+instance r.setoid : Setoid (M × S) where
+  R := r S M
+  iseqv := ⟨(r.isEquiv S M).refl, (r.isEquiv S M).symm, (r.isEquiv S M).trans⟩
+#align localized_module.r.setoid LocalizedModule.r.setoid
 
 -- TODO: change `localization` to use `r'` instead of `r` so that the two types are also defeq,
 -- `localization S = localized_module S R`.
-example {R} [CommSemiring R] (S : Submonoid R) : ⇑(Localization.r' S) = LocalizedModule.R S R :=
+example {R} [CommSemiring R] (S : Submonoid R) : ⇑(Localization.r' S) = LocalizedModule.r S R :=
   rfl
 
+#print LocalizedModule /-
 /-- If `S` is a multiplicative subset of a ring `R` and `M` an `R`-module, then
 we can localize `M` by `S`.
 -/
 @[nolint has_nonempty_instance]
 def LocalizedModule : Type max u v :=
-  Quotient (R.setoid S M)
+  Quotient (r.setoid S M)
 #align localized_module LocalizedModule
+-/
 
 section
 
 variable {M S}
 
+/- warning: localized_module.mk -> LocalizedModule.mk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localized_module.mk LocalizedModule.mkₓ'. -/
 /-- The canonical map sending `(m, s) ↦ m/s`-/
 def mk (m : M) (s : S) : LocalizedModule S M :=
   Quotient.mk' ⟨m, s⟩
 #align localized_module.mk LocalizedModule.mk
 
+/- warning: localized_module.mk_eq -> LocalizedModule.mk_eq is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align localized_module.mk_eq LocalizedModule.mk_eqₓ'. -/
 theorem mk_eq {m m' : M} {s s' : S} : mk m s = mk m' s' ↔ ∃ u : S, u • s' • m = u • s • m' :=
   Quotient.eq'
 #align localized_module.mk_eq LocalizedModule.mk_eq
 
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+Case conversion may be inaccurate. Consider using '#align localized_module.induction_on LocalizedModule.induction_onₓ'. -/
 @[elab_as_elim]
 theorem induction_on {β : LocalizedModule S M → Prop} (h : ∀ (m : M) (s : S), β (mk m s)) :
     ∀ x : LocalizedModule S M, β x := by
@@ -106,6 +144,12 @@ theorem induction_on {β : LocalizedModule S M → Prop} (h : ∀ (m : M) (s : S
   exact h m s
 #align localized_module.induction_on LocalizedModule.induction_on
 
+/- warning: localized_module.induction_on₂ -> LocalizedModule.induction_on₂ is a dubious translation:
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 @[elab_as_elim]
 theorem induction_on₂ {β : LocalizedModule S M → LocalizedModule S M → Prop}
     (h : ∀ (m m' : M) (s s' : S), β (mk m s) (mk m' s')) : ∀ x y, β x y :=
@@ -114,6 +158,12 @@ theorem induction_on₂ {β : LocalizedModule S M → LocalizedModule S M → Pr
   exact h m m' s s'
 #align localized_module.induction_on₂ LocalizedModule.induction_on₂
 
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+Case conversion may be inaccurate. Consider using '#align localized_module.lift_on LocalizedModule.liftOnₓ'. -/
 /-- If `f : M × S → α` respects the equivalence relation `localized_module.r`, then
 `f` descents to a map `localized_module M S → α`.
 -/
@@ -122,10 +172,22 @@ def liftOn {α : Type _} (x : LocalizedModule S M) (f : M × S → α)
   Quotient.liftOn x f wd
 #align localized_module.lift_on LocalizedModule.liftOn
 
+/- warning: localized_module.lift_on_mk -> LocalizedModule.liftOn_mk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localized_module.lift_on_mk LocalizedModule.liftOn_mkₓ'. -/
 theorem liftOn_mk {α : Type _} {f : M × S → α} (wd : ∀ (p p' : M × S) (h1 : p ≈ p'), f p = f p')
     (m : M) (s : S) : liftOn (mk m s) f wd = f ⟨m, s⟩ := by convert Quotient.liftOn_mk f wd ⟨m, s⟩
 #align localized_module.lift_on_mk LocalizedModule.liftOn_mk
 
+/- warning: localized_module.lift_on₂ -> LocalizedModule.liftOn₂ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localized_module.lift_on₂ LocalizedModule.liftOn₂ₓ'. -/
 /-- If `f : M × S → M × S → α` respects the equivalence relation `localized_module.r`, then
 `f` descents to a map `localized_module M S → localized_module M S → α`.
 -/
@@ -134,6 +196,12 @@ def liftOn₂ {α : Type _} (x y : LocalizedModule S M) (f : M × S → M × S 
   Quotient.liftOn₂ x y f wd
 #align localized_module.lift_on₂ LocalizedModule.liftOn₂
 
+/- warning: localized_module.lift_on₂_mk -> LocalizedModule.liftOn₂_mk is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align localized_module.lift_on₂_mk LocalizedModule.liftOn₂_mkₓ'. -/
 theorem liftOn₂_mk {α : Type _} (f : M × S → M × S → α)
     (wd : ∀ (p q p' q' : M × S) (h1 : p ≈ p') (h2 : q ≈ q'), f p q = f p' q') (m m' : M)
     (s s' : S) : liftOn₂ (mk m s) (mk m' s') f wd = f ⟨m, s⟩ ⟨m', s'⟩ := by
@@ -143,6 +211,12 @@ theorem liftOn₂_mk {α : Type _} (f : M × S → M × S → α)
 instance : Zero (LocalizedModule S M) :=
   ⟨mk 0 1⟩
 
+/- warning: localized_module.zero_mk -> LocalizedModule.zero_mk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localized_module.zero_mk LocalizedModule.zero_mkₓ'. -/
 @[simp]
 theorem zero_mk (s : S) : mk (0 : M) s = 0 :=
   mk_eq.mpr ⟨1, by rw [one_smul, smul_zero, smul_zero, one_smul]⟩
@@ -162,6 +236,12 @@ instance : Add (LocalizedModule S M)
             hu1' hu2'⊢
           rw [hu1', hu2']⟩
 
+/- warning: localized_module.mk_add_mk -> LocalizedModule.mk_add_mk is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {m1 : M} {m2 : M} {s1 : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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+Case conversion may be inaccurate. Consider using '#align localized_module.mk_add_mk LocalizedModule.mk_add_mkₓ'. -/
 theorem mk_add_mk {m1 m2 : M} {s1 s2 : S} :
     mk m1 s1 + mk m2 s2 = mk (s2 • m1 + s1 • m2) (s1 * s2) :=
   mk_eq.mpr <| ⟨1, by dsimp only <;> rw [one_smul]⟩
@@ -201,8 +281,10 @@ private theorem add_zero' (x : LocalizedModule S M) : x + 0 = x :=
     x
 #align localized_module.add_zero' localized_module.add_zero'
 
+#print LocalizedModule.hasNatSmul /-
 instance hasNatSmul : SMul ℕ (LocalizedModule S M) where smul n := nsmulRec n
 #align localized_module.has_nat_smul LocalizedModule.hasNatSmul
+-/
 
 private theorem nsmul_zero' (x : LocalizedModule S M) : (0 : ℕ) • x = 0 :=
   LocalizedModule.induction_on (fun _ _ => rfl) x
@@ -246,6 +328,12 @@ instance {M : Type _} [AddCommGroup M] [Module R M] : AddCommGroup (LocalizedMod
       rw [lift_on_mk, mk_add_mk]
       simp }
 
+/- warning: localized_module.mk_neg -> LocalizedModule.mk_neg is a dubious translation:
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 theorem mk_neg {M : Type _} [AddCommGroup M] [Module R M] {m : M} {s : S} : mk (-m) s = -mk m s :=
   rfl
 #align localized_module.mk_neg LocalizedModule.mk_neg
@@ -333,6 +421,12 @@ instance {A : Type _} [CommRing A] [Algebra R A] {S : Submonoid R} :
       obtain ⟨⟨a₂, s₂⟩, rfl : mk a₂ s₂ = x₂⟩ := Quotient.exists_rep x₂
       exact mk_eq.mpr ⟨1, by simp only [one_smul, mul_comm]⟩ }
 
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s₁ s₂))
+but is expected to have type
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(Algebra.toModule.{u2, u1} R A _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_4 _inst_5)) 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(CommSemiring.toSemiring.{u2} R _inst_1)))) S)) s₁ s₂))
+Case conversion may be inaccurate. Consider using '#align localized_module.mk_mul_mk LocalizedModule.mk_mul_mkₓ'. -/
 theorem mk_mul_mk {A : Type _} [Semiring A] [Algebra R A] {a₁ a₂ : A} {s₁ s₂ : S} :
     mk a₁ s₁ * mk a₂ s₂ = mk (a₁ * a₂) (s₁ * s₂) :=
   rfl
@@ -361,6 +455,12 @@ instance : SMul (Localization S) (LocalizedModule S M)
         ring_nf  at eq1'⊢
         rw [eq1'])
 
+/- warning: localized_module.mk_smul_mk -> LocalizedModule.mk_smul_mk is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) S)) s t))
+Case conversion may be inaccurate. Consider using '#align localized_module.mk_smul_mk LocalizedModule.mk_smul_mkₓ'. -/
 theorem mk_smul_mk (r : R) (m : M) (s t : S) : Localization.mk r s • mk m t = mk (r • m) (s * t) :=
   by
   unfold SMul.smul
@@ -425,6 +525,12 @@ private theorem zero_smul' (x : LocalizedModule S M) : (0 : Localization S) •
   rw [← Localization.mk_zero s, mk_smul_mk, zero_smul, zero_mk]
 #align localized_module.zero_smul' localized_module.zero_smul'
 
+/- warning: localized_module.is_module -> LocalizedModule.isModule is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2], Module.{u1, max u1 u2} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) S) (Localization.commSemiring.{u1} R _inst_1 S)) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align localized_module.is_module LocalizedModule.isModuleₓ'. -/
 instance isModule : Module (Localization S) (LocalizedModule S M)
     where
   smul := (· • ·)
@@ -436,6 +542,12 @@ instance isModule : Module (Localization S) (LocalizedModule S M)
   zero_smul := zero_smul'
 #align localized_module.is_module LocalizedModule.isModule
 
+/- warning: localized_module.mk_cancel_common_left -> LocalizedModule.mk_cancel_common_left is a dubious translation:
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s' s)) (LocalizedModule.mk.{u1, u2} R _inst_1 S M _inst_2 _inst_3 m s)
+Case conversion may be inaccurate. Consider using '#align localized_module.mk_cancel_common_left LocalizedModule.mk_cancel_common_leftₓ'. -/
 @[simp]
 theorem mk_cancel_common_left (s' s : S) (m : M) : mk (s' • m) (s' * s) = mk m s :=
   mk_eq.mpr
@@ -444,20 +556,44 @@ theorem mk_cancel_common_left (s' s : S) (m : M) : mk (s' • m) (s' * s) = mk m
       rw [smul_comm]⟩
 #align localized_module.mk_cancel_common_left LocalizedModule.mk_cancel_common_left
 
+/- warning: localized_module.mk_cancel -> LocalizedModule.mk_cancel is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align localized_module.mk_cancel LocalizedModule.mk_cancelₓ'. -/
 @[simp]
 theorem mk_cancel (s : S) (m : M) : mk (s • m) s = mk m 1 :=
   mk_eq.mpr ⟨1, by simp⟩
 #align localized_module.mk_cancel LocalizedModule.mk_cancel
 
+/- warning: localized_module.mk_cancel_common_right -> LocalizedModule.mk_cancel_common_right is a dubious translation:
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s s')) (LocalizedModule.mk.{u1, u2} R _inst_1 S M _inst_2 _inst_3 m s)
+Case conversion may be inaccurate. Consider using '#align localized_module.mk_cancel_common_right LocalizedModule.mk_cancel_common_rightₓ'. -/
 @[simp]
 theorem mk_cancel_common_right (s s' : S) (m : M) : mk (s' • m) (s * s') = mk m s :=
   mk_eq.mpr ⟨1, by simp [mul_smul]⟩
 #align localized_module.mk_cancel_common_right LocalizedModule.mk_cancel_common_right
 
+/- warning: localized_module.is_module' -> LocalizedModule.isModule' is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2], Module.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align localized_module.is_module' LocalizedModule.isModule'ₓ'. -/
 instance isModule' : Module R (LocalizedModule S M) :=
   { Module.compHom (LocalizedModule S M) <| algebraMap R (Localization S) with }
 #align localized_module.is_module' LocalizedModule.isModule'
 
+/- warning: localized_module.smul'_mk -> LocalizedModule.smul'_mk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localized_module.smul'_mk LocalizedModule.smul'_mkₓ'. -/
 theorem smul'_mk (r : R) (s : S) (m : M) : r • mk m s = mk (r • m) s := by
   erw [mk_smul_mk r m 1 s, one_mul]
 #align localized_module.smul'_mk LocalizedModule.smul'_mk
@@ -479,6 +615,12 @@ instance {A : Type _} [Semiring A] [Algebra R A] : Algebra (Localization S) (Loc
       rw [mk_mul_mk, ← Localization.mk_eq_mk', mk_smul_mk, mk_smul_mk, mk_mul_mk, mul_left_comm,
         mul_smul_comm])
 
+/- warning: localized_module.algebra_map_mk -> LocalizedModule.algebraMap_mk is a dubious translation:
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+but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun 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(LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S)) (RingHom.instRingHomClassRingHom.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S))) (Semiring.toNonAssocSemiring.{max u2 u1} (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S)))))) (algebraMap.{u2, max u2 u1} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S) (LocalizedModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5)) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 S) (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5 S) (LocalizedModule.instAlgebraLocalizationToCommMonoidLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleInstCommSemiringLocalizationToCommMonoidInstSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4 _inst_5)) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) S a s)) (LocalizedModule.mk.{u2, u1} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_4))) (Algebra.toModule.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) _inst_1 _inst_4 _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_4))))) (algebraMap.{u2, u1} R A _inst_1 _inst_4 _inst_5) a) s)
+Case conversion may be inaccurate. Consider using '#align localized_module.algebra_map_mk LocalizedModule.algebraMap_mkₓ'. -/
 theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
     algebraMap _ _ (Localization.mk a s) = mk (algebraMap R A a) s :=
   by
@@ -490,6 +632,12 @@ theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
 instance : IsScalarTower R (Localization S) (LocalizedModule S M) :=
   RestrictScalars.isScalarTower R (Localization S) (LocalizedModule S M)
 
+/- warning: localized_module.algebra' -> LocalizedModule.algebra' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {A : Type.{u2}} [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4], Algebra.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) _inst_1 (LocalizedModule.semiring.{u1, u2} R _inst_1 A _inst_4 _inst_5 S)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {A : Type.{u2}} [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4], Algebra.{u1, max u2 u1} R (LocalizedModule.{u1, u2} R _inst_1 S A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)) _inst_1 (LocalizedModule.instSemiringLocalizedModuleToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModule.{u1, u2} R _inst_1 A _inst_4 _inst_5 S)
+Case conversion may be inaccurate. Consider using '#align localized_module.algebra' LocalizedModule.algebra'ₓ'. -/
 instance algebra' {A : Type _} [Semiring A] [Algebra R A] : Algebra R (LocalizedModule S A) :=
   { (algebraMap (Localization S) (LocalizedModule S A)).comp (algebraMap R <| Localization S),
     show Module R (LocalizedModule S A) by
@@ -512,6 +660,12 @@ section
 
 variable (S M)
 
+/- warning: localized_module.mk_linear_map -> LocalizedModule.mkLinearMap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (M : Type.{u2}) [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2], LinearMap.{u1, u1, u2, max 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))) M (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _inst_2 (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _inst_3 (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (M : Type.{u2}) [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2], LinearMap.{u1, u1, u2, max u2 u1} 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 (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _inst_2 (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) _inst_3 (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3)
+Case conversion may be inaccurate. Consider using '#align localized_module.mk_linear_map LocalizedModule.mkLinearMapₓ'. -/
 /-- The function `m ↦ m / 1` as an `R`-linear map.
 -/
 @[simps]
@@ -524,6 +678,12 @@ def mkLinearMap : M →ₗ[R] LocalizedModule S M
 
 end
 
+/- warning: localized_module.div_by -> LocalizedModule.divBy is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2], (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) S) -> (LinearMap.{u1, u1, max u1 u2, max 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.addCommMonoid.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2], (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x S)) -> (LinearMap.{u1, u1, max u2 u1, max u2 u1} 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))) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3) (LocalizedModule.isModule'.{u1, u2} R _inst_1 S M _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align localized_module.div_by LocalizedModule.divByₓ'. -/
 /-- For any `s : S`, there is an `R`-linear map given by `a/b ↦ a/(b*s)`.
 -/
 @[simps]
@@ -549,6 +709,12 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M
       simp [LocalizedModule.liftOn_mk, smul'_mk]
 #align localized_module.div_by LocalizedModule.divBy
 
+/- warning: localized_module.div_by_mul_by -> LocalizedModule.divBy_mul_by is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align localized_module.div_by_mul_by LocalizedModule.divBy_mul_byₓ'. -/
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
     divBy s (algebraMap R (Module.End R (LocalizedModule S M)) s p) = p :=
   p.inductionOn
@@ -558,6 +724,12 @@ theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
       erw [mk_cancel_common_left s t])
 #align localized_module.div_by_mul_by LocalizedModule.divBy_mul_by
 
+/- warning: localized_module.mul_by_div_by -> LocalizedModule.mul_by_divBy is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align localized_module.mul_by_div_by LocalizedModule.mul_by_divByₓ'. -/
 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
     algebraMap R (Module.End R (LocalizedModule S M)) s (divBy s p) = p :=
   p.inductionOn
@@ -581,6 +753,7 @@ variable {M M' M'' : Type _} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid
 
 variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
+#print IsLocalizedModule /-
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
@@ -593,9 +766,16 @@ class IsLocalizedModule : Prop where
   surj : ∀ y : M', ∃ x : M × S, x.2 • y = f x.1
   eq_iff_exists : ∀ {x₁ x₂}, f x₁ = f x₂ ↔ ∃ c : S, c • x₂ = c • x₁
 #align is_localized_module IsLocalizedModule
+-/
 
 namespace LocalizedModule
 
+/- warning: localized_module.lift' -> LocalizedModule.lift' is a dubious translation:
+lean 3 declaration is
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(NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) -> (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M''
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4], (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) -> (forall (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x)) (Module.End.monoid.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R 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(RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) S)) x))) -> (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M''
+Case conversion may be inaccurate. Consider using '#align localized_module.lift' LocalizedModule.lift'ₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 there is a linear map `localized_module S M → M''`.
@@ -630,11 +810,23 @@ noncomputable def lift' (g : M →ₗ[R] M'')
     rfl
 #align localized_module.lift' LocalizedModule.lift'
 
+/- warning: localized_module.lift'_mk -> LocalizedModule.lift'_mk is a dubious translation:
+lean 3 declaration is
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(NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (h s)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) => M -> M'') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) g m))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u1} M'' (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (LocalizedModule.mk.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 m s)) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun 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+Case conversion may be inaccurate. Consider using '#align localized_module.lift'_mk LocalizedModule.lift'_mkₓ'. -/
 theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (m : M) (s : S) : LocalizedModule.lift' S g h (LocalizedModule.mk m s) = (h s).Unit⁻¹.1 (g m) :=
   rfl
 #align localized_module.lift'_mk LocalizedModule.lift'_mk
 
+/- warning: localized_module.lift'_add -> LocalizedModule.lift'_add is a dubious translation:
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(LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (instHAdd.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.hasAdd.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) x y)) (HAdd.hAdd.{u3, u3, u3} M'' M'' M'' (instHAdd.{u3} M'' (AddZeroClass.toHasAdd.{u3} M'' (AddMonoid.toAddZeroClass.{u3} M'' (AddCommMonoid.toAddMonoid.{u3} M'' _inst_4)))) (LocalizedModule.lift'.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h x) (LocalizedModule.lift'.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h y))
+but is expected to have type
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(x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (y : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u1} M'' (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (instHAdd.{max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) x y)) (HAdd.hAdd.{u1, u1, u1} M'' M'' M'' (instHAdd.{u1} M'' (AddZeroClass.toAdd.{u1} M'' (AddMonoid.toAddZeroClass.{u1} M'' (AddCommMonoid.toAddMonoid.{u1} M'' _inst_4)))) (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h x) (LocalizedModule.lift'.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h y))
+Case conversion may be inaccurate. Consider using '#align localized_module.lift'_add LocalizedModule.lift'_addₓ'. -/
 theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (x y) :
     LocalizedModule.lift' S g h (x + y) =
@@ -652,6 +844,12 @@ theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
     x y
 #align localized_module.lift'_add LocalizedModule.lift'_add
 
+/- warning: localized_module.lift'_smul -> LocalizedModule.lift'_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_7 : Module.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (fun (_x : RingHom.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) => R -> (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)) (RingHom.hasCoeToFun.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7))) (algebraMap.{u1, u3} R (Module.End.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.algebra.{u1, u3} R M'' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_4 _inst_7)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) (r : R) (m : LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u3} M'' (SMul.smul.{u1, u3} R M'' (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 (Ring.toSemiring.{u1} R (CommRing.toRing.{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 (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M'' (AddMonoid.toAddZeroClass.{u3} M'' (AddCommMonoid.toAddMonoid.{u3} M'' _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7)))) r (LocalizedModule.lift'.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h m)) (LocalizedModule.lift'.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h (SMul.smul.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toHasSmul.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddZeroClass.toHasZero.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5))))) r m))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} 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_inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, 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+Case conversion may be inaccurate. Consider using '#align localized_module.lift'_smul LocalizedModule.lift'_smulₓ'. -/
 theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (r : R) (m) : r • LocalizedModule.lift' S g h m = LocalizedModule.lift' S g h (r • m) :=
   m.inductionOn
@@ -662,6 +860,12 @@ theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (
       erw [← h1.unit⁻¹.1.map_smul, ← g.map_smul])
 #align localized_module.lift'_smul LocalizedModule.lift'_smul
 
+/- warning: localized_module.lift -> LocalizedModule.lift is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7)
+Case conversion may be inaccurate. Consider using '#align localized_module.lift LocalizedModule.liftₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 there is a linear map `localized_module S M → M''`.
@@ -674,6 +878,12 @@ noncomputable def lift (g : M →ₗ[R] M'')
   map_smul' r x := by rw [LocalizedModule.lift'_smul, RingHom.id_apply]
 #align localized_module.lift LocalizedModule.lift
 
+/- warning: localized_module.lift_mk -> LocalizedModule.lift_mk is a dubious translation:
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(Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) s)) (h s)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) => M -> M'') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) g m))
+but is expected to have type
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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (m : M) (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M'') (LocalizedModule.mk.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 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+Case conversion may be inaccurate. Consider using '#align localized_module.lift_mk LocalizedModule.lift_mkₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 `lift g m s = s⁻¹ • g m`.
@@ -683,6 +893,12 @@ theorem lift_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Mod
   rfl
 #align localized_module.lift_mk LocalizedModule.lift_mk
 
+/- warning: localized_module.lift_comp -> LocalizedModule.lift_comp is a dubious translation:
+lean 3 declaration is
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(LinearMap.comp.{u1, u1, u1, u2, max u1 u2, u3} R R R M (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_4 _inst_5 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LocalizedModule.lift.{u1, u2, u3} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) (LocalizedModule.mkLinearMap.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) g
+but is expected to have type
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(x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomCompTriple.ids.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LocalizedModule.lift.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) (LocalizedModule.mkLinearMap.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) g
+Case conversion may be inaccurate. Consider using '#align localized_module.lift_comp LocalizedModule.lift_compₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
 there is a linear map `lift g ∘ mk_linear_map = g`.
@@ -694,6 +910,12 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
   erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, one_smul]
 #align localized_module.lift_comp LocalizedModule.lift_comp
 
+/- warning: localized_module.lift_unique -> LocalizedModule.lift_unique is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M'' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : AddCommMonoid.{u1} M''] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_7 : Module.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x)) (Module.End.monoid.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u3, u1} R (Module.End.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u3} R _inst_1) (Module.End.semiring.{u3, u1} R M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R M'' (CommRing.toCommSemiring.{u3} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) S)) x))) (l : LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7), (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u3, u3, u3, u2, max u3 u2, u1} R R R M (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 _inst_5 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomCompTriple.ids.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) l (LocalizedModule.mkLinearMap.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) g) -> (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M'' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_4 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_7) (LocalizedModule.lift.{u3, u2, u1} R _inst_1 S M M'' _inst_2 _inst_4 _inst_5 _inst_7 g h) l)
+Case conversion may be inaccurate. Consider using '#align localized_module.lift_unique LocalizedModule.lift_uniqueₓ'. -/
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible and
 `l` is another linear map `localized_module S M ⟶ M''` such that `l ∘ mk_linear_map = g` then
@@ -712,6 +934,12 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
 
 end LocalizedModule
 
+/- warning: localized_module_is_localized_module -> localizedModuleIsLocalizedModule is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2], IsLocalizedModule.{u1, u2, max u1 u2} R _inst_1 S M (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_2 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_5 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.mkLinearMap.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2], IsLocalizedModule.{u1, u2, max u1 u2} R _inst_1 S M (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_2 (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_5 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.mkLinearMap.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align localized_module_is_localized_module localizedModuleIsLocalizedModuleₓ'. -/
 instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule.mkLinearMap S M)
     where
   map_units s :=
@@ -739,6 +967,7 @@ namespace IsLocalizedModule
 
 variable [IsLocalizedModule S f]
 
+#print IsLocalizedModule.fromLocalizedModule' /-
 /-- If `(M', f : M ⟶ M')` satisfies universal property of localized module, there is a canonical map
 `localized_module S M ⟶ M'`.
 -/
@@ -752,7 +981,14 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
         Module.End_algebraMap_isUnit_inv_apply_eq_iff', ← LinearMap.map_smul, ← LinearMap.map_smul]
       exact (IsLocalizedModule.eq_iff_exists S f).mpr ⟨c, eq1⟩)
 #align is_localized_module.from_localized_module' IsLocalizedModule.fromLocalizedModule'
+-/
 
+/- warning: is_localized_module.from_localized_module'_mk -> IsLocalizedModule.fromLocalizedModule'_mk is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ 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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R 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+Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_mk IsLocalizedModule.fromLocalizedModule'_mkₓ'. -/
 @[simp]
 theorem fromLocalizedModule'_mk (m : M) (s : S) :
     fromLocalizedModule' S f (LocalizedModule.mk m s) =
@@ -760,6 +996,12 @@ theorem fromLocalizedModule'_mk (m : M) (s : S) :
   rfl
 #align is_localized_module.from_localized_module'_mk IsLocalizedModule.fromLocalizedModule'_mk
 
+/- warning: is_localized_module.from_localized_module'_add -> IsLocalizedModule.fromLocalizedModule'_add is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (x : LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (y : LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u3} M' (IsLocalizedModule.fromLocalizedModule'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (instHAdd.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.hasAdd.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) x y)) (HAdd.hAdd.{u3, u3, u3} M' M' M' (instHAdd.{u3} M' (AddZeroClass.toHasAdd.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3)))) (IsLocalizedModule.fromLocalizedModule'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 x) (IsLocalizedModule.fromLocalizedModule'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 y))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (y : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u1} M' (IsLocalizedModule.fromLocalizedModule'.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (instHAdd.{max u3 u2} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instAddLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) x y)) (HAdd.hAdd.{u1, u1, u1} M' M' M' (instHAdd.{u1} M' (AddZeroClass.toAdd.{u1} M' (AddMonoid.toAddZeroClass.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)))) (IsLocalizedModule.fromLocalizedModule'.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 x) (IsLocalizedModule.fromLocalizedModule'.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 y))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_add IsLocalizedModule.fromLocalizedModule'_addₓ'. -/
 theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
     fromLocalizedModule' S f (x + y) = fromLocalizedModule' S f x + fromLocalizedModule' S f y :=
   LocalizedModule.induction_on₂
@@ -780,6 +1022,12 @@ theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
     x y
 #align is_localized_module.from_localized_module'_add IsLocalizedModule.fromLocalizedModule'_add
 
+/- warning: is_localized_module.from_localized_module'_smul -> IsLocalizedModule.fromLocalizedModule'_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (r : R) (x : LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u3} M' (SMul.smul.{u1, u3} R M' (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) r (IsLocalizedModule.fromLocalizedModule'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 x)) (IsLocalizedModule.fromLocalizedModule'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (SMul.smul.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toHasSmul.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddZeroClass.toHasZero.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u2} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5))))) r x))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (r : R) (x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5), Eq.{succ u1} M' (HSMul.hSMul.{u3, u1, u1} R M' M' (instHSMul.{u3, u1} R M' (SMulZeroClass.toSMul.{u3, u1} R M' (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6))))) r (IsLocalizedModule.fromLocalizedModule'.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 x)) (IsLocalizedModule.fromLocalizedModule'.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 (HSMul.hSMul.{u3, max u3 u2, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (instHSMul.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulZeroClass.toSMul.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.instZeroLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (SMulWithZero.toSMulZeroClass.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.instZeroLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MulActionWithZero.toSMulWithZero.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LocalizedModule.instZeroLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (Module.toMulActionWithZero.{u3, max u3 u2} R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)))))) r x))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module'_smul IsLocalizedModule.fromLocalizedModule'_smulₓ'. -/
 theorem fromLocalizedModule'_smul (r : R) (x : LocalizedModule S M) :
     r • fromLocalizedModule' S f x = fromLocalizedModule' S f (r • x) :=
   LocalizedModule.induction_on
@@ -790,6 +1038,12 @@ theorem fromLocalizedModule'_smul (r : R) (x : LocalizedModule S M) :
     x
 #align is_localized_module.from_localized_module'_smul IsLocalizedModule.fromLocalizedModule'_smul
 
+/- warning: is_localized_module.from_localized_module -> IsLocalizedModule.fromLocalizedModule is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], LinearMap.{u1, u1, max u2 u1, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6
+Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module IsLocalizedModule.fromLocalizedModuleₓ'. -/
 /-- If `(M', f : M ⟶ M')` satisfies universal property of localized module, there is a canonical map
 `localized_module S M ⟶ M'`.
 -/
@@ -800,12 +1054,24 @@ noncomputable def fromLocalizedModule : LocalizedModule S M →ₗ[R] M'
   map_smul' r x := by rw [from_localized_module'_smul, RingHom.id_apply]
 #align is_localized_module.from_localized_module IsLocalizedModule.fromLocalizedModule
 
+/- warning: is_localized_module.from_localized_module_mk -> IsLocalizedModule.fromLocalizedModule_mk is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s : coeSort.{succ u1, succ (succ 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module_mk IsLocalizedModule.fromLocalizedModule_mkₓ'. -/
 theorem fromLocalizedModule_mk (m : M) (s : S) :
     fromLocalizedModule S f (LocalizedModule.mk m s) =
       (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
   rfl
 #align is_localized_module.from_localized_module_mk IsLocalizedModule.fromLocalizedModule_mk
 
+/- warning: is_localized_module.from_localized_module.inj -> IsLocalizedModule.fromLocalizedModule.inj is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.injₓ'. -/
 theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f := fun x y eq1 =>
   by
   induction' x using LocalizedModule.induction_on with a b
@@ -818,6 +1084,12 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
   rfl
 #align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.inj
 
+/- warning: is_localized_module.from_localized_module.surj -> IsLocalizedModule.fromLocalizedModule.surj is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Surjective.{succ (max u1 u2), succ u3} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Surjective.{max (succ u3) (succ u2), succ u1} (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u3, u3, max u2 u3, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6) (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (fun (_x : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u2, u1} R R (LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.surj IsLocalizedModule.fromLocalizedModule.surjₓ'. -/
 theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S f := fun x =>
   let ⟨⟨m, s⟩, eq1⟩ := IsLocalizedModule.surj S f x
   ⟨LocalizedModule.mk m s,
@@ -826,10 +1098,22 @@ theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S
     rfl⟩
 #align is_localized_module.from_localized_module.surj IsLocalizedModule.fromLocalizedModule.surj
 
+/- warning: is_localized_module.from_localized_module.bij -> IsLocalizedModule.fromLocalizedModule.bij is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Bijective.{succ (max u1 u2), succ u3} (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) (fun (_x : LinearMap.{u1, u1, max u1 u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6) => (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) -> M') (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.fromLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.from_localized_module.bij IsLocalizedModule.fromLocalizedModule.bijₓ'. -/
 theorem fromLocalizedModule.bij : Function.Bijective <| fromLocalizedModule S f :=
   ⟨fromLocalizedModule.inj _ _, fromLocalizedModule.surj _ _⟩
 #align is_localized_module.from_localized_module.bij IsLocalizedModule.fromLocalizedModule.bij
 
+/- warning: is_localized_module.iso -> IsLocalizedModule.iso is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], LinearEquiv.{u1, u1, max u2 u1, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (LocalizedModule.instAddCommMonoidLocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6
+Case conversion may be inaccurate. Consider using '#align is_localized_module.iso IsLocalizedModule.isoₓ'. -/
 /--
 If `(M', f : M ⟶ M')` satisfies universal property of localized module, then `M'` is isomorphic to
 `localized_module S M` as an `R`-module.
@@ -840,11 +1124,23 @@ noncomputable def iso : LocalizedModule S M ≃ₗ[R] M' :=
     Equiv.ofBijective (fromLocalizedModule S f) <| fromLocalizedModule.bij _ _ with }
 #align is_localized_module.iso IsLocalizedModule.iso
 
+/- warning: is_localized_module.iso_apply_mk -> IsLocalizedModule.iso_apply_mk is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_apply_mk IsLocalizedModule.iso_apply_mkₓ'. -/
 theorem iso_apply_mk (m : M) (s : S) :
     iso S f (LocalizedModule.mk m s) = (IsLocalizedModule.map_units f s).Unit⁻¹ (f m) :=
   rfl
 #align is_localized_module.iso_apply_mk IsLocalizedModule.iso_apply_mk
 
+/- warning: is_localized_module.iso_symm_apply_aux -> IsLocalizedModule.iso_symm_apply_aux is a dubious translation:
+lean 3 declaration is
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(IsLocalizedModule.surj.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m))))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M'), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M') => LocalizedModule.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) m) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearEquiv.{u3, u3, u1, max u3 u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' 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+Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_apply_aux IsLocalizedModule.iso_symm_apply_auxₓ'. -/
 theorem iso_symm_apply_aux (m : M') :
     (iso S f).symm m =
       LocalizedModule.mk (IsLocalizedModule.surj S f m).some.1
@@ -857,6 +1153,12 @@ theorem iso_symm_apply_aux (m : M') :
   erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff', h2.some_spec]
 #align is_localized_module.iso_symm_apply_aux IsLocalizedModule.iso_symm_apply_aux
 
+/- warning: is_localized_module.iso_symm_apply' -> IsLocalizedModule.iso_symm_apply' is a dubious translation:
+lean 3 declaration is
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(IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) => M' -> (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max u1 u2} R R M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8)) m) (LocalizedModule.mk.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5 a b))
+but is expected to have type
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_inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M') (a : M) (b : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), (Eq.{succ u2} M' (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R 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(MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) M' (Submonoid.smul.{u3, u2} R M' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, u2} R M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M' (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) b m) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M' _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, max u3 u1} R R M' (LocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 (LocalizedModule.instAddCommMonoidLocalizedModule.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IsLocalizedModule.iso.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8)) m) (LocalizedModule.mk.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5 a b))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'ₓ'. -/
 theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
     (iso S f).symm m = LocalizedModule.mk a b :=
   (iso_symm_apply_aux S f m).trans <|
@@ -866,12 +1168,24 @@ theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
         mul_smul, mul_comm, mul_smul, eq1]
 #align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'
 
+/- warning: is_localized_module.iso_symm_comp -> IsLocalizedModule.iso_symm_comp is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Eq.{max (succ u2) (succ (max u1 u2))} (LinearMap.{u1, u1, u2, max u1 u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_2 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_5 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)) (LinearMap.comp.{u1, u1, u1, u2, u3, max u1 u2} R R R M M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_5 _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearEquiv.toLinearMap.{u1, u1, u3, max u1 u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) M' (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) (LinearEquiv.symm.{u1, u1, max u1 u2, u3} R R (LocalizedModule.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LocalizedModule.addCommMonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_3 (LocalizedModule.isModule'.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (IsLocalizedModule.iso._proof_1.{u1} R _inst_1) (IsLocalizedModule.iso._proof_2.{u1} R _inst_1) (IsLocalizedModule.iso.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))) f) (LocalizedModule.mkLinearMap.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S M _inst_2 _inst_5)
+but is expected to have type
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(RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IsLocalizedModule.iso.{u3, u2, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))) f) (LocalizedModule.mkLinearMap.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S M _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_localized_module.iso_symm_comp IsLocalizedModule.iso_symm_compₓ'. -/
 theorem iso_symm_comp : (iso S f).symm.toLinearMap.comp f = LocalizedModule.mkLinearMap S M :=
   by
   ext m; rw [LinearMap.comp_apply, LocalizedModule.mkLinearMap_apply]
   change (iso S f).symm _ = _; rw [iso_symm_apply']; exact one_smul _ _
 #align is_localized_module.iso_symm_comp IsLocalizedModule.iso_symm_comp
 
+/- warning: is_localized_module.lift -> IsLocalizedModule.lift is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.lift IsLocalizedModule.liftₓ'. -/
 /--
 If `M'` is a localized module and `g` is a linear map `M' → M''` such that all scalar multiplication
 by `s : S` is invertible, then there is a linear map `M' → M''`.
@@ -881,6 +1195,12 @@ noncomputable def lift (g : M →ₗ[R] M'')
   (LocalizedModule.lift S g h).comp (iso S f).symm.toLinearMap
 #align is_localized_module.lift IsLocalizedModule.lift
 
+/- warning: is_localized_module.lift_comp -> IsLocalizedModule.lift_comp is a dubious translation:
+lean 3 declaration is
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_inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsLocalizedModule.lift.{u1, u2, u3, u4} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) f) g
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u3}} {M' : Type.{u1}} {M'' : Type.{u2}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_4 : AddCommMonoid.{u2} M''] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u1} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u2} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))), Eq.{max (succ u3) (succ u2)} (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u3, u1, u2} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (IsLocalizedModule.lift.{u4, u3, u1, u2} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) f) g
+Case conversion may be inaccurate. Consider using '#align is_localized_module.lift_comp IsLocalizedModule.lift_compₓ'. -/
 theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x)) :
     (lift S f g h).comp f = g :=
   by
@@ -890,6 +1210,12 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
   exact iso_symm_comp _ _
 #align is_localized_module.lift_comp IsLocalizedModule.lift_comp
 
+/- warning: is_localized_module.lift_unique -> IsLocalizedModule.lift_unique is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} {M'' : Type.{u4}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_4 : AddCommMonoid.{u4} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] [_inst_7 : Module.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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(Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) (l : LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7), (Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M M' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) l f) g) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) (IsLocalizedModule.lift.{u1, u2, u3, u4} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) l)
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u3}} {M' : Type.{u1}} {M'' : Type.{u2}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_4 : AddCommMonoid.{u2} M''] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u1} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (h : forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => 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(Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) 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(CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) l f) g) -> (Eq.{max (succ u1) (succ u2)} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) (IsLocalizedModule.lift.{u4, u3, u1, u2} R _inst_1 S M M' M'' _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f _inst_8 g h) l)
+Case conversion may be inaccurate. Consider using '#align is_localized_module.lift_unique IsLocalizedModule.lift_uniqueₓ'. -/
 theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (l : M' →ₗ[R] M'') (hl : l.comp f = g) : lift S f g h = l :=
   by
@@ -904,6 +1230,12 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
     erw [from_localized_module_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, one_smul]
 #align is_localized_module.lift_unique IsLocalizedModule.lift_unique
 
+/- warning: is_localized_module.is_universal -> IsLocalizedModule.is_universal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} {M'' : Type.{u4}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_4 : AddCommMonoid.{u4} M''] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] [_inst_7 : Module.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7), (forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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_inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M M' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) l f) g))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u3}} {M' : Type.{u1}} {M'' : Type.{u2}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_4 : AddCommMonoid.{u2} M''] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u1} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (g : LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7), (forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7))) R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)) (RingHom.instRingHomClassRingHom.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7)))))) (algebraMap.{u4, u2} R (Module.End.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (CommRing.toCommSemiring.{u4} R _inst_1) (Module.End.semiring.{u4, u2} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Module.instAlgebraEndToSemiringSemiring.{u4, u2} R M'' (CommRing.toCommSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))) -> (ExistsUnique.{max (succ u1) (succ u2)} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) (fun (l : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) => Eq.{max (succ u3) (succ u2)} (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u3, u1, u2} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) l f) g))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.is_universal IsLocalizedModule.is_universalₓ'. -/
 /-- Universal property from localized module:
 If `(M', f : M ⟶ M')` is a localized module then it satisfies the following universal property:
 For every `R`-module `M''` which every `s : S`-scalar multiplication is invertible and for every
@@ -924,6 +1256,12 @@ theorem is_universal :
   fun g h => ⟨lift S f g h, lift_comp S f g h, fun l hl => (lift_unique S f g h l hl).symm⟩
 #align is_localized_module.is_universal IsLocalizedModule.is_universal
 
+/- warning: is_localized_module.ring_hom_ext -> IsLocalizedModule.ringHom_ext is a dubious translation:
+lean 3 declaration is
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_inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], (forall (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), IsUnit.{u4} (Module.End.{u1, u4} R M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_7) (Module.End.monoid.{u1, u4} R M'' (Ring.toSemiring.{u1} 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(NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x S))))) x))) -> (forall {{j : LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}} {{k : LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}}, (Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M M' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) j f) (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M M' M'' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) k f)) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) j k))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) {M : Type.{u1}} {M' : Type.{u2}} {M'' : Type.{u3}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_4 : AddCommMonoid.{u3} M''] [_inst_5 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2] [_inst_6 : Module.{u4, u2} R M' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_3] [_inst_7 : Module.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4] (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u4, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], (forall (x : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) x S)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Module.End.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (Subtype.val.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Set.{u4} R) (Set.instMembershipSet.{u4} R) x (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x)) (Module.End.monoid.{u4, u3} R M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_4 _inst_7) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R 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(Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) S)) x))) -> (forall {{j : LinearMap.{u4, u4, u2, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}} {{k : LinearMap.{u4, u4, u2, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7}}, (Eq.{max (succ u1) (succ u3)} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M M'' _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.comp.{u4, u4, u4, u1, u2, u3} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) j f) (LinearMap.comp.{u4, u4, u4, u1, u2, u3} R R R M M' M'' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomCompTriple.ids.{u4, u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) k f)) -> (Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) M' M'' _inst_3 _inst_4 _inst_6 _inst_7) j k))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.ring_hom_ext IsLocalizedModule.ringHom_extₓ'. -/
 theorem ringHom_ext (map_unit : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     ⦃j k : M' →ₗ[R] M''⦄ (h : j.comp f = k.comp f) : j = k :=
   by
@@ -931,34 +1269,66 @@ theorem ringHom_ext (map_unit : ∀ x : S, IsUnit ((algebraMap R (Module.End R M
   rfl
 #align is_localized_module.ring_hom_ext IsLocalizedModule.ringHom_ext
 
+#print IsLocalizedModule.linearEquiv /-
 /-- If `(M', f)` and `(M'', g)` both satisfy universal property of localized module, then `M', M''`
 are isomorphic as `R`-module
 -/
 noncomputable def linearEquiv [IsLocalizedModule S g] : M' ≃ₗ[R] M'' :=
   (iso S f).symm.trans (iso S g)
 #align is_localized_module.linear_equiv IsLocalizedModule.linearEquiv
+-/
 
 variable {S}
 
+/- warning: is_localized_module.smul_injective -> IsLocalizedModule.smul_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Function.Injective.{succ u3, succ u3} M' M' (fun (m : M') => SMul.smul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (Submonoid.hasSmul.{u1, u3} R M' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) S) s m)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {M : Type.{u3}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2] [_inst_6 : Module.{u2, u1} R M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3] (f : LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u2, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)), Function.Injective.{succ u1, succ u1} M' M' (fun (m : M') => HSMul.hSMul.{u2, u1, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) M' M' (instHSMul.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) M' (Submonoid.smul.{u2, u1} R M' (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (SMulZeroClass.toSMul.{u2, u1} R M' (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M' (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M' (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 _inst_6)))) S)) s m)
+Case conversion may be inaccurate. Consider using '#align is_localized_module.smul_injective IsLocalizedModule.smul_injectiveₓ'. -/
 theorem smul_injective (s : S) : Function.Injective fun m : M' => s • m :=
   ((Module.End_isUnit_iff _).mp (IsLocalizedModule.map_units f s)).Injective
 #align is_localized_module.smul_injective IsLocalizedModule.smul_injective
 
+/- warning: is_localized_module.smul_inj -> IsLocalizedModule.smul_inj is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (m₁ : M') (m₂ : M'), Iff (Eq.{succ u3} M' (SMul.smul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (Submonoid.hasSmul.{u1, u3} R M' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) S) s m₁) (SMul.smul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (Submonoid.hasSmul.{u1, u3} R M' (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u3} R M' (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M' (AddMonoid.toAddZeroClass.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3 _inst_6)))) S) s m₂)) (Eq.{succ u3} M' m₁ m₂)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {M : Type.{u3}} {M' : Type.{u1}} [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_2] [_inst_6 : Module.{u2, u1} R M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3] (f : LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u2, u3, u1} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) (m₁ : M') (m₂ : M'), Iff (Eq.{succ u1} M' (HSMul.hSMul.{u2, u1, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) M' M' (instHSMul.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) M' (Submonoid.smul.{u2, u1} R M' (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (SMulZeroClass.toSMul.{u2, u1} R M' (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M' (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M' (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 _inst_6)))) S)) s m₁) (HSMul.hSMul.{u2, u1, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) M' M' (instHSMul.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x S)) M' (Submonoid.smul.{u2, u1} R M' (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (SMulZeroClass.toSMul.{u2, u1} R M' (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M' (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M' (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M' (AddCommMonoid.toAddMonoid.{u1} M' _inst_3)) (Module.toMulActionWithZero.{u2, u1} R M' (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 _inst_6)))) S)) s m₂)) (Eq.{succ u1} M' m₁ m₂)
+Case conversion may be inaccurate. Consider using '#align is_localized_module.smul_inj IsLocalizedModule.smul_injₓ'. -/
 theorem smul_inj (s : S) (m₁ m₂ : M') : s • m₁ = s • m₂ ↔ m₁ = m₂ :=
   (smul_injective f s).eq_iff
 #align is_localized_module.smul_inj IsLocalizedModule.smul_inj
 
+/- warning: is_localized_module.mk' -> IsLocalizedModule.mk' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], M -> (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) -> M'
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], M -> (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) -> M'
+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk' IsLocalizedModule.mk'ₓ'. -/
 /-- `mk' f m s` is the fraction `m/s` with respect to the localization map `f`. -/
 noncomputable def mk' (m : M) (s : S) : M' :=
   fromLocalizedModule S f (LocalizedModule.mk m s)
 #align is_localized_module.mk' IsLocalizedModule.mk'
 
+/- warning: is_localized_module.mk'_smul -> IsLocalizedModule.mk'_smul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_smul IsLocalizedModule.mk'_smulₓ'. -/
 theorem mk'_smul (r : R) (m : M) (s : S) : mk' f (r • m) s = r • mk' f m s :=
   by
   delta mk'
   rw [← LocalizedModule.smul'_mk, LinearMap.map_smul]
 #align is_localized_module.mk'_smul IsLocalizedModule.mk'_smul
 
+/- warning: is_localized_module.mk'_add_mk' -> IsLocalizedModule.mk'_add_mk' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_add_mk' IsLocalizedModule.mk'_add_mk'ₓ'. -/
 theorem mk'_add_mk' (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ + mk' f m₂ s₂ = mk' f (s₂ • m₁ + s₁ • m₂) (s₁ * s₂) :=
   by
@@ -966,12 +1336,24 @@ theorem mk'_add_mk' (m₁ m₂ : M) (s₁ s₂ : S) :
   rw [← map_add, LocalizedModule.mk_add_mk]
 #align is_localized_module.mk'_add_mk' IsLocalizedModule.mk'_add_mk'
 
+/- warning: is_localized_module.mk'_zero -> IsLocalizedModule.mk'_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_zero IsLocalizedModule.mk'_zeroₓ'. -/
 @[simp]
 theorem mk'_zero (s : S) : mk' f 0 s = 0 := by rw [← zero_smul R (0 : M), mk'_smul, zero_smul]
 #align is_localized_module.mk'_zero IsLocalizedModule.mk'_zero
 
 variable (S)
 
+/- warning: is_localized_module.mk'_one -> IsLocalizedModule.mk'_one is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_one IsLocalizedModule.mk'_oneₓ'. -/
 @[simp]
 theorem mk'_one (m : M) : mk' f m (1 : S) = f m :=
   by
@@ -982,6 +1364,12 @@ theorem mk'_one (m : M) : mk' f m (1 : S) = f m :=
 
 variable {S}
 
+/- warning: is_localized_module.mk'_cancel -> IsLocalizedModule.mk'_cancel is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f m)
+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancelₓ'. -/
 @[simp]
 theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m :=
   by
@@ -990,11 +1378,23 @@ theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m :=
   rfl
 #align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancel
 
+/- warning: is_localized_module.mk'_cancel' -> IsLocalizedModule.mk'_cancel' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel' IsLocalizedModule.mk'_cancel'ₓ'. -/
 @[simp]
 theorem mk'_cancel' (m : M) (s : S) : s • mk' f m s = f m := by
   rw [Submonoid.smul_def, ← mk'_smul, ← Submonoid.smul_def, mk'_cancel]
 #align is_localized_module.mk'_cancel' IsLocalizedModule.mk'_cancel'
 
+/- warning: is_localized_module.mk'_cancel_left -> IsLocalizedModule.mk'_cancel_left is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel_left IsLocalizedModule.mk'_cancel_leftₓ'. -/
 @[simp]
 theorem mk'_cancel_left (m : M) (s₁ s₂ : S) : mk' f (s₁ • m) (s₁ * s₂) = mk' f m s₂ :=
   by
@@ -1002,6 +1402,12 @@ theorem mk'_cancel_left (m : M) (s₁ s₂ : S) : mk' f (s₁ • m) (s₁ * s
   rw [LocalizedModule.mk_cancel_common_left]
 #align is_localized_module.mk'_cancel_left IsLocalizedModule.mk'_cancel_left
 
+/- warning: is_localized_module.mk'_cancel_right -> IsLocalizedModule.mk'_cancel_right is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m : M) (s₁ : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) (s₂ : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_cancel_right IsLocalizedModule.mk'_cancel_rightₓ'. -/
 @[simp]
 theorem mk'_cancel_right (m : M) (s₁ s₂ : S) : mk' f (s₂ • m) (s₁ * s₂) = mk' f m s₁ :=
   by
@@ -1009,10 +1415,22 @@ theorem mk'_cancel_right (m : M) (s₁ s₂ : S) : mk' f (s₂ • m) (s₁ * s
   rw [LocalizedModule.mk_cancel_common_right]
 #align is_localized_module.mk'_cancel_right IsLocalizedModule.mk'_cancel_right
 
+/- warning: is_localized_module.mk'_add -> IsLocalizedModule.mk'_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_add IsLocalizedModule.mk'_addₓ'. -/
 theorem mk'_add (m₁ m₂ : M) (s : S) : mk' f (m₁ + m₂) s = mk' f m₁ s + mk' f m₂ s := by
   rw [mk'_add_mk', ← smul_add, mk'_cancel_left]
 #align is_localized_module.mk'_add IsLocalizedModule.mk'_add
 
+/- warning: is_localized_module.mk'_eq_mk'_iff -> IsLocalizedModule.mk'_eq_mk'_iff is a dubious translation:
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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Iff (Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m₁ s₁) (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m₂ s₂)) (Exists.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) (fun (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) => Eq.{succ u2} M (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M (Submonoid.hasSmul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_5)))) S) s (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M (Submonoid.hasSmul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_5)))) S) s₁ m₂)) (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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(MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_5)))) S) s (SMul.smul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M (Submonoid.hasSmul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2 _inst_5)))) S) s₂ m₁))))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {M : Type.{u1}} {M' : Type.{u2}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} M'] [_inst_5 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2] [_inst_6 : Module.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3] (f : LinearMap.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] (m₁ : M) (m₂ : M) (s₁ : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) (s₂ : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m₁ s₁) (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m₂ s₂)) (Exists.{succ u3} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R 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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_mk'_iff IsLocalizedModule.mk'_eq_mk'_iffₓ'. -/
 theorem mk'_eq_mk'_iff (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ = mk' f m₂ s₂ ↔ ∃ s : S, s • s₁ • m₂ = s • s₂ • m₁ :=
   by
@@ -1021,6 +1439,12 @@ theorem mk'_eq_mk'_iff (m₁ m₂ : M) (s₁ s₂ : S) :
   simp_rw [eq_comm]
 #align is_localized_module.mk'_eq_mk'_iff IsLocalizedModule.mk'_eq_mk'_iff
 
+/- warning: is_localized_module.mk'_neg -> IsLocalizedModule.mk'_neg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_9 : AddCommGroup.{u2} M] [_inst_10 : AddCommGroup.{u3} M'] [_inst_11 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_9)] [_inst_12 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_10)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_9) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_10) _inst_11 _inst_12) [_inst_13 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_9) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_10) _inst_11 _inst_12 f] (m : M) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S), Eq.{succ u3} M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_9) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_10) _inst_11 _inst_12 f _inst_13 (Neg.neg.{u2} M (SubNegMonoid.toHasNeg.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_9))) m) s) (Neg.neg.{u3} M' (SubNegMonoid.toHasNeg.{u3} M' (AddGroup.toSubNegMonoid.{u3} M' (AddCommGroup.toAddGroup.{u3} M' _inst_10))) (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_9) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_10) _inst_11 _inst_12 f _inst_13 m s))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_neg IsLocalizedModule.mk'_negₓ'. -/
 theorem mk'_neg {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m : M) (s : S) : mk' f (-m) s = -mk' f m s :=
   by
@@ -1028,18 +1452,36 @@ theorem mk'_neg {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M]
   rw [LocalizedModule.mk_neg, map_neg]
 #align is_localized_module.mk'_neg IsLocalizedModule.mk'_neg
 
+/- warning: is_localized_module.mk'_sub -> IsLocalizedModule.mk'_sub is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_sub IsLocalizedModule.mk'_subₓ'. -/
 theorem mk'_sub {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m₁ m₂ : M) (s : S) :
     mk' f (m₁ - m₂) s = mk' f m₁ s - mk' f m₂ s := by
   rw [sub_eq_add_neg, sub_eq_add_neg, mk'_add, mk'_neg]
 #align is_localized_module.mk'_sub IsLocalizedModule.mk'_sub
 
+/- warning: is_localized_module.mk'_sub_mk' -> IsLocalizedModule.mk'_sub_mk' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {M : Type.{u3}} {M' : Type.{u2}} [_inst_9 : AddCommGroup.{u3} M] [_inst_10 : AddCommGroup.{u2} M'] [_inst_11 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_9)] [_inst_12 : Module.{u1, u2} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_10)] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_9) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_10) _inst_11 _inst_12) [_inst_13 : IsLocalizedModule.{u1, u3, u2} R _inst_1 S M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_9) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_10) _inst_11 _inst_12 f] (m₁ : M) (m₂ : M) (s₁ : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_sub_mk' IsLocalizedModule.mk'_sub_mk'ₓ'. -/
 theorem mk'_sub_mk' {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ - mk' f m₂ s₂ = mk' f (s₂ • m₁ - s₁ • m₂) (s₁ * s₂) := by
   rw [sub_eq_add_neg, ← mk'_neg, mk'_add_mk', smul_neg, ← sub_eq_add_neg]
 #align is_localized_module.mk'_sub_mk' IsLocalizedModule.mk'_sub_mk'
 
+/- warning: is_localized_module.mk'_mul_mk'_of_map_mul -> IsLocalizedModule.mk'_mul_mk'_of_map_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {M : Type.{u2}} {M' : Type.{u3}} [_inst_9 : Semiring.{u2} M] [_inst_10 : Semiring.{u3} M'] [_inst_11 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} M (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} M (Semiring.toNonAssocSemiring.{u2} M _inst_9)))] [_inst_12 : Algebra.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) _inst_10] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_mul_mk'_of_map_mul IsLocalizedModule.mk'_mul_mk'_of_map_mulₓ'. -/
 theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Module R M]
     [Algebra R M'] (f : M →ₗ[R] M') (hf : ∀ m₁ m₂, f (m₁ * m₂) = f m₁ * f m₂)
     [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
@@ -1052,6 +1494,12 @@ theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Modul
   simp_rw [← Submonoid.smul_def, mk'_cancel, smul_eq_mul, hf]
 #align is_localized_module.mk'_mul_mk'_of_map_mul IsLocalizedModule.mk'_mul_mk'_of_map_mul
 
+/- warning: is_localized_module.mk'_mul_mk' -> IsLocalizedModule.mk'_mul_mk' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_mul_mk' IsLocalizedModule.mk'_mul_mk'ₓ'. -/
 theorem mk'_mul_mk' {M M' : Type _} [Semiring M] [Semiring M'] [Algebra R M] [Algebra R M']
     (f : M →ₐ[R] M') [IsLocalizedModule S f.toLinearMap] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f.toLinearMap m₁ s₁ * mk' f.toLinearMap m₂ s₂ = mk' f.toLinearMap (m₁ * m₂) (s₁ * s₂) :=
@@ -1060,21 +1508,45 @@ theorem mk'_mul_mk' {M M' : Type _} [Semiring M] [Semiring M'] [Algebra R M] [Al
 
 variable {f}
 
+/- warning: is_localized_module.mk'_eq_iff -> IsLocalizedModule.mk'_eq_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M' (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_3 _inst_6)))) S)) s m'))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_iff IsLocalizedModule.mk'_eq_iffₓ'. -/
 @[simp]
 theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m' := by
   rw [← smul_inj f s, Submonoid.smul_def, ← mk'_smul, ← Submonoid.smul_def, mk'_cancel]
 #align is_localized_module.mk'_eq_iff IsLocalizedModule.mk'_eq_iff
 
+/- warning: is_localized_module.mk'_eq_zero -> IsLocalizedModule.mk'_eq_zero is a dubious translation:
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 @[simp]
 theorem mk'_eq_zero {m : M} (s : S) : mk' f m s = 0 ↔ f m = 0 := by rw [mk'_eq_iff, smul_zero]
 #align is_localized_module.mk'_eq_zero IsLocalizedModule.mk'_eq_zero
 
 variable (f)
 
+/- warning: is_localized_module.mk'_eq_zero' -> IsLocalizedModule.mk'_eq_zero' is a dubious translation:
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_inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M} (s : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)), Iff (Eq.{succ u2} M' (IsLocalizedModule.mk'.{u3, u1, u2} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8 m s) (OfNat.ofNat.{u2} M' 0 (Zero.toOfNat0.{u2} M' (AddMonoid.toZero.{u2} M' (AddCommMonoid.toAddMonoid.{u2} M' _inst_3))))) (Exists.{succ u3} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) x S)) (fun (s' : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R 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(AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_2 _inst_5)))) S)) s' m) (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_eq_zero' IsLocalizedModule.mk'_eq_zero'ₓ'. -/
 theorem mk'_eq_zero' {m : M} (s : S) : mk' f m s = 0 ↔ ∃ s' : S, s' • m = 0 := by
   simp_rw [← mk'_zero f (1 : S), mk'_eq_mk'_iff, smul_zero, one_smul, eq_comm]
 #align is_localized_module.mk'_eq_zero' IsLocalizedModule.mk'_eq_zero'
 
+/- warning: is_localized_module.mk_eq_mk' -> IsLocalizedModule.mk_eq_mk' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk_eq_mk' IsLocalizedModule.mk_eq_mk'ₓ'. -/
 theorem mk_eq_mk' (s : S) (m : M) :
     LocalizedModule.mk m s = mk' (LocalizedModule.mkLinearMap S M) m s := by
   rw [eq_comm, mk'_eq_iff, Submonoid.smul_def, LocalizedModule.smul'_mk, ← Submonoid.smul_def,
@@ -1083,10 +1555,22 @@ theorem mk_eq_mk' (s : S) (m : M) :
 
 variable (S)
 
+/- warning: is_localized_module.eq_zero_iff -> IsLocalizedModule.eq_zero_iff is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f] {m : M}, Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f m) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (AddMonoid.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) (AddCommMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') m) _inst_3))))) (Exists.{succ u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (fun (s' : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) => Eq.{succ u2} M (HSMul.hSMul.{u1, u2, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M M (instHSMul.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) M (Submonoid.smul.{u1, u2} R M (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_2 _inst_5)))) S)) s' m) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.eq_zero_iff IsLocalizedModule.eq_zero_iffₓ'. -/
 theorem eq_zero_iff {m : M} : f m = 0 ↔ ∃ s' : S, s' • m = 0 :=
   (mk'_eq_zero (1 : S)).symm.trans (mk'_eq_zero' f _)
 #align is_localized_module.eq_zero_iff IsLocalizedModule.eq_zero_iff
 
+/- warning: is_localized_module.mk'_surjective -> IsLocalizedModule.mk'_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {M : Type.{u2}} {M' : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_2] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' _inst_2 _inst_3 _inst_5 _inst_6) [_inst_8 : IsLocalizedModule.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f], Function.Surjective.{max (succ u2) (succ u1), succ u3} (Prod.{u2, u1} M (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S)) M' (Function.uncurry.{u2, u1, u3} M (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) S) M' (IsLocalizedModule.mk'.{u1, u2, u3} R _inst_1 S M M' _inst_2 _inst_3 _inst_5 _inst_6 f _inst_8))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk'_surjective IsLocalizedModule.mk'_surjectiveₓ'. -/
 theorem mk'_surjective : Function.Surjective (Function.uncurry <| mk' f : M × S → M') :=
   by
   intro x
@@ -1096,6 +1580,12 @@ theorem mk'_surjective : Function.Surjective (Function.uncurry <| mk' f : M × S
 
 section Algebra
 
+/- warning: is_localized_module.mk_of_algebra -> IsLocalizedModule.mkOfAlgebra is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {S' : Type.{u3}} [_inst_9 : CommRing.{u1} R] [_inst_10 : CommRing.{u2} S] [_inst_11 : CommRing.{u3} S'] [_inst_12 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10))] [_inst_13 : Algebra.{u1, u3} R S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11))] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) (f : AlgHom.{u1, u2, u3} R S S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_12 _inst_13), (forall (x : R), (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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_inst_9)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))))) M) S (Submonoid.hasSmul.{u1, u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_9))))) (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 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))) (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 (CommRing.toCommSemiring.{u1} R _inst_9)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) _inst_12))))) M) m x) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_10)))))))))))) -> (IsLocalizedModule.{u1, u2, u3} R _inst_9 M S S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u1, u3} R S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_13) (AlgHom.toLinearMap.{u1, u2, u3} R S S' (CommRing.toCommSemiring.{u1} R _inst_9) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_10)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_11)) _inst_12 _inst_13 f))
+but is expected to have type
+  forall {R : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_9 : CommRing.{u3} R] [_inst_10 : CommRing.{u2} S] [_inst_11 : CommRing.{u1} S'] [_inst_12 : Algebra.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))] [_inst_13 : Algebra.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (f : AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13), (forall (x : R), (Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') x) _inst_11)))) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S') _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))) R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))) (RingHom.instRingHomClassRingHom.{u3, u1} R S' (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))) (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (algebraMap.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) x))) -> (forall (y : S'), Exists.{max (succ u3) (succ u2)} (Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M))) (fun (x : Prod.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M))) => Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') (Prod.fst.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x)) (HSMul.hSMul.{u3, u1, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S' ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') (Prod.fst.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x)) (instHSMul.{u3, u1} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S' (Submonoid.smul.{u3, u1} R S' (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (Algebra.toSMul.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) M)) (Prod.snd.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12))))) (SMulZeroClass.toSMul.{u3, u1} R S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribMulAction.toDistribSMul.{u3, u1} R S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12)) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R S S' (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHomClass.linearMapClass.{u3, u2, u1, max u2 u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (AlgHom.algHomClass.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13))))) f (Prod.fst.{u2, u3} S (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) x)))) -> (forall (x : S), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (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 (CommRing.toCommSemiring.{u2} S _inst_10))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R S (AddMonoid.toAddZeroClass.{u2} S 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(CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12))))) (SMulZeroClass.toSMul.{u3, u1} R S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))))) (DistribMulAction.toDistribSMul.{u3, u1} R S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) R S S' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)))))) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12)) (Module.toDistribMulAction.{u3, u1} R S' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13)) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, u1, max u2 u1} R S S' (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHomClass.linearMapClass.{u3, u2, u1, max u2 u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 (AlgHom.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13) (AlgHom.algHomClass.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13))))) f x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') x) _inst_11)))))) -> (Exists.{succ u3} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) (fun (m : Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) => Eq.{succ u2} S (HSMul.hSMul.{u3, u2, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S S (instHSMul.{u3, u2} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9)))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))))) x M)) S (Submonoid.smul.{u3, u2} R S (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_9))))) (Algebra.toSMul.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) M)) m x) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)))))))) -> (IsLocalizedModule.{u3, u2, u1} R _inst_9 M S S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) _inst_12) (Algebra.toModule.{u3, u1} R S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_13) (AlgHom.toLinearMap.{u3, u2, u1} R S S' (CommRing.toCommSemiring.{u3} R _inst_9) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_10)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_11)) _inst_12 _inst_13 f))
+Case conversion may be inaccurate. Consider using '#align is_localized_module.mk_of_algebra IsLocalizedModule.mkOfAlgebraₓ'. -/
 theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [Algebra R S]
     [Algebra R S'] (M : Submonoid R) (f : S →ₐ[R] S') (h₁ : ∀ x ∈ M, IsUnit (algebraMap R S' x))
     (h₂ : ∀ y, ∃ x : S × M, x.2 • y = f x.1) (h₃ : ∀ x, f x = 0 → ∃ m : M, m • x = 0) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -581,9 +581,9 @@ variable {M M' M'' : Type _} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid
 
 variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`map_units] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`surj] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`eq_iff_exists] [] -/
 /-- The characteristic predicate for localized module.
 `is_localized_module S f` describes that `f : M ⟶ M'` is the localization map identifying `M'` as
 `localized_module S M`.

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

@@ -287,11 +287,11 @@ instance {A : Type _} [Semiring A] [Algebra R A] {S : Submonoid R} :
     zero_mul := by
       intro x
       obtain ⟨⟨a, s⟩, rfl : mk a s = x⟩ := Quotient.exists_rep x
-      exact mk_eq.mpr ⟨1, by simp only [zero_mul, smul_zero]⟩
+      exact mk_eq.mpr ⟨1, by simp only [MulZeroClass.zero_mul, smul_zero]⟩
     mul_zero := by
       intro x
       obtain ⟨⟨a, s⟩, rfl : mk a s = x⟩ := Quotient.exists_rep x
-      exact mk_eq.mpr ⟨1, by simp only [mul_zero, smul_zero]⟩
+      exact mk_eq.mpr ⟨1, by simp only [MulZeroClass.mul_zero, smul_zero]⟩
     mul_assoc := by
       intro x₁ x₂ x₃
       obtain ⟨⟨a₁, s₁⟩, rfl : mk a₁ s₁ = x₁⟩ := Quotient.exists_rep x₁

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -254,7 +254,8 @@ instance {A : Type*} [Semiring A] [Algebra R A] {S : Submonoid R} :
           dsimp only at e₁ e₂ ⊢
           rw [eq_comm]
           trans (u₁ • t₁ • a₁) • u₂ • t₂ • a₂
-          rw [e₁, e₂]; swap; rw [eq_comm]
+          on_goal 1 => rw [e₁, e₂]
+          on_goal 2 => rw [eq_comm]
           all_goals
             rw [smul_smul, mul_mul_mul_comm, ← smul_eq_mul, ← smul_eq_mul A, smul_smul_smul_comm,
               mul_smul, mul_smul])

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -1160,3 +1160,5 @@ theorem mkOfAlgebra {R S S' : Type*} [CommRing R] [CommRing S] [CommRing S'] [Al
 end Algebra
 
 end IsLocalizedModule
+
+end IsLocalizedModule

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -900,6 +900,10 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
   rw [LinearMap.comp_assoc, iso_symm_comp, LocalizedModule.lift_comp S g h]
 #align is_localized_module.lift_comp IsLocalizedModule.lift_comp
 
+@[simp]
+theorem lift_apply (g : M →ₗ[R] M'') (h) (x) :
+    lift S f g h (f x) = g x := LinearMap.congr_fun (lift_comp S f g h) x
+
 theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (l : M' →ₗ[R] M'') (hl : l.comp f = g) : lift S f g h = l := by
   dsimp only [IsLocalizedModule.lift]
@@ -1102,6 +1106,28 @@ theorem mk'_surjective : Function.Surjective (Function.uncurry <| mk' f : M × S
   exact ⟨⟨m, s⟩, mk'_eq_iff.mpr e.symm⟩
 #align is_localized_module.mk'_surjective IsLocalizedModule.mk'_surjective
 
+variable {N N'} [AddCommGroup N] [AddCommGroup N'] [Module R N] [Module R N']
+variable (g : N →ₗ[R] N') [IsLocalizedModule S g]
+
+/-- A linear map `M →ₗ[R] N` gives a map between localized modules `Mₛ →ₗ[R] Nₛ`. -/
+noncomputable
+def map : (M →ₗ[R] N) →ₗ[R] (M' →ₗ[R] N') where
+  toFun h := lift S f (g ∘ₗ h) (IsLocalizedModule.map_units g)
+  map_add' h₁ h₂ := by
+    apply IsLocalizedModule.ringHom_ext S f (IsLocalizedModule.map_units g)
+    simp only [lift_comp, LinearMap.add_comp, LinearMap.comp_add]
+  map_smul' r h := by
+    apply IsLocalizedModule.ringHom_ext S f (IsLocalizedModule.map_units g)
+    simp only [lift_comp, LinearMap.add_comp, LinearMap.comp_add, LinearMap.smul_comp,
+      LinearMap.comp_smul, RingHom.id_apply]
+
+lemma map_comp (h : M →ₗ[R] N) : (map S f g h) ∘ₗ f = g ∘ₗ h :=
+  lift_comp S f (g ∘ₗ h) (IsLocalizedModule.map_units g)
+
+@[simp]
+lemma map_apply (h : M →ₗ[R] N) (x) : map S f g h (f x) = g (h x) :=
+  lift_apply S f (g ∘ₗ h) (IsLocalizedModule.map_units g) x
+
 section Algebra
 
 theorem mkOfAlgebra {R S S' : Type*} [CommRing R] [CommRing S] [CommRing S'] [Algebra R S]

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.

@@ -77,7 +77,7 @@ example {R} [CommSemiring R] (S : Submonoid R) : ⇑(Localization.r' S) = Locali
 /-- If `S` is a multiplicative subset of a ring `R` and `M` an `R`-module, then
 we can localize `M` by `S`.
 -/
--- Porting note: @[nolint has_nonempty_instance]
+-- Porting note(#5171): @[nolint has_nonempty_instance]
 def _root_.LocalizedModule : Type max u v :=
   Quotient (r.setoid S M)
 #align localized_module LocalizedModule

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -204,7 +204,7 @@ instance hasNatSMul : SMul ℕ (LocalizedModule S M) where smul n := nsmulRec n
 private theorem nsmul_zero' (x : LocalizedModule S M) : (0 : ℕ) • x = 0 :=
   LocalizedModule.induction_on (fun _ _ => rfl) x
 
-private theorem nsmul_succ' (n : ℕ) (x : LocalizedModule S M) : n.succ • x = x + n • x :=
+private theorem nsmul_succ' (n : ℕ) (x : LocalizedModule S M) : n.succ • x = n • x + x :=
   LocalizedModule.induction_on (fun _ _ => rfl) x
 
 instance : AddCommMonoid (LocalizedModule S M) where

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)

@@ -42,9 +42,7 @@ namespace LocalizedModule
 universe u v
 
 variable {R : Type u} [CommSemiring R] (S : Submonoid R)
-
 variable (M : Type v) [AddCommMonoid M] [Module R M]
-
 variable (T : Type*) [CommSemiring T] [Algebra R T] [IsLocalization S T]
 
 /-- The equivalence relation on `M × S` where `(m1, s1) ≈ (m2, s2)` if and only if
@@ -544,13 +542,9 @@ section IsLocalizedModule
 universe u v
 
 variable {R : Type*} [CommSemiring R] (S : Submonoid R)
-
 variable {M M' M'' : Type*} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid M'']
-
 variable {A : Type*} [CommSemiring A] [Algebra R A] [Module A M'] [IsLocalization S A]
-
 variable [Module R M] [Module R M'] [Module R M''] [IsScalarTower R A M']
-
 variable (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
 /-- The characteristic predicate for localized module.

This PR removes the default values for nsmul and zsmul, forcing the user to populate them manually. The previous behavior can be obtained by writing nsmul := nsmulRec and zsmul := zsmulRec, which is now in the docstring for these fields.

The motivation here is to make it more obvious when module diamonds are being introduced, or at least where they might be hiding; you can now simply search for nsmulRec in the source code.

Arguably we should do the same thing for intCast, natCast, pow, and zpow too, but diamonds are less common in those fields, so I'll leave them to a subsequent PR.

Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -220,12 +220,14 @@ instance : AddCommMonoid (LocalizedModule S M) where
   nsmul_succ := nsmul_succ'
   add_comm := add_comm'
 
+instance {M : Type*} [AddCommGroup M] [Module R M] : Neg (LocalizedModule S M) where
+  neg p :=
+    liftOn p (fun x => LocalizedModule.mk (-x.1) x.2) fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => by
+      rw [mk_eq]
+      exact ⟨u, by simpa⟩
+
 instance {M : Type*} [AddCommGroup M] [Module R M] : AddCommGroup (LocalizedModule S M) :=
   { show AddCommMonoid (LocalizedModule S M) by infer_instance with
-    neg := fun p =>
-      liftOn p (fun x => LocalizedModule.mk (-x.1) x.2) fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => by
-        rw [mk_eq]
-        exact ⟨u, by simpa⟩
     add_left_neg := by
       rintro ⟨m, s⟩
       change
@@ -235,7 +237,9 @@ instance {M : Type*} [AddCommGroup M] [Module R M] : AddCommGroup (LocalizedModu
             mk m s =
           0
       rw [liftOn_mk, mk_add_mk]
-      simp }
+      simp
+    -- TODO: fix the diamond
+    zsmul := zsmulRec }
 
 theorem mk_neg {M : Type*} [AddCommGroup M] [Module R M] {m : M} {s : S} : mk (-m) s = -mk m s :=
   rfl

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -607,7 +607,7 @@ theorem isLocalizedModule_iff_isLocalization {A Aₛ} [CommSemiring A] [Algebra
   refine and_congr ?_ (and_congr (forall_congr' fun _ ↦ ?_) (forall₂_congr fun _ _ ↦ ?_))
   · simp_rw [← (Algebra.lmul R Aₛ).commutes, Algebra.lmul_isUnit_iff, Subtype.forall,
       Algebra.algebraMapSubmonoid, ← SetLike.mem_coe, Submonoid.coe_map,
-      Set.ball_image_iff, ← IsScalarTower.algebraMap_apply]
+      Set.forall_mem_image, ← IsScalarTower.algebraMap_apply]
   · simp_rw [Prod.exists, Subtype.exists, Algebra.algebraMapSubmonoid]
     simp [← IsScalarTower.algebraMap_apply, Submonoid.mk_smul, Algebra.smul_def, mul_comm]
   · congr!; simp_rw [Subtype.exists, Algebra.algebraMapSubmonoid]; simp [Algebra.smul_def]

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -1062,7 +1062,7 @@ theorem mk'_mul_mk' {M M' : Type*} [Semiring M] [Semiring M'] [Algebra R M] [Alg
 
 variable {f}
 
-/-- Porting note: simp can prove this
+/-- Porting note (#10618): simp can prove this
 @[simp] -/
 theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m' := by
   rw [← smul_inj f s, Submonoid.smul_def, ← mk'_smul, ← Submonoid.smul_def, mk'_cancel]

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -510,8 +510,8 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M where
     refine x.induction_on (fun _ _ ↦ ?_)
     dsimp only
     change liftOn (mk _ _) _ _ = r • (liftOn (mk _ _) _ _)
-    simp_rw [RingHom.toMonoidHom_eq_coe, OneHom.toFun_eq_coe, MonoidHom.toOneHom_coe,
-      MonoidHom.coe_coe, ZeroHom.coe_mk, liftOn_mk, mul_assoc, ← smul_def, algebraMap_smul]
+    simp_rw [liftOn_mk, mul_assoc, ← smul_def]
+    congr!
 #align localized_module.div_by LocalizedModule.divBy
 
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
@@ -519,8 +519,9 @@ theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
   p.induction_on fun m t => by
     rw [Module.algebraMap_end_apply, divBy_apply]
     erw [smul_def]
-    rw [LocalizedModule.liftOn_mk, mul_assoc, ← smul_def, ZeroHom.coe_mk, RingHom.toFun_eq_coe,
-      algebraMap_smul, smul'_mk, ← Submonoid.smul_def, mk_cancel_common_right _ s]
+    rw [LocalizedModule.liftOn_mk, mul_assoc, ← smul_def]
+    erw [smul'_mk]
+    rw [← Submonoid.smul_def, mk_cancel_common_right _ s]
 #align localized_module.div_by_mul_by LocalizedModule.divBy_mul_by
 
 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang, Jujian Zhang
 -/
 import Mathlib.Algebra.Algebra.Bilinear
-import Mathlib.Algebra.Algebra.RestrictScalars
 import Mathlib.RingTheory.Localization.Basic
 
 #align_import algebra.module.localized_module from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -741,9 +741,9 @@ instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule
     where
   map_units s :=
     ⟨⟨algebraMap R (Module.End R (LocalizedModule S M)) s, LocalizedModule.divBy s,
-        FunLike.ext _ _ <| LocalizedModule.mul_by_divBy s,
-        FunLike.ext _ _ <| LocalizedModule.divBy_mul_by s⟩,
-      FunLike.ext _ _ fun p =>
+        DFunLike.ext _ _ <| LocalizedModule.mul_by_divBy s,
+        DFunLike.ext _ _ <| LocalizedModule.divBy_mul_by s⟩,
+      DFunLike.ext _ _ fun p =>
         p.induction_on <| by
           intros
           rfl⟩

In particular, LocalizedModule.induction_on uses LocalizedModule.mk rather than Quotient.mk.

@@ -508,35 +508,27 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M where
     simp_rw [mk_add_mk, LocalizedModule.liftOn_mk, mk_add_mk, mul_smul, mul_comm _ s, mul_assoc,
       smul_comm _ s, ← smul_add, mul_left_comm s t₁ t₂, mk_cancel_common_left s]
   map_smul' r x := by
-    refine x.inductionOn (fun _ ↦ ?_)
+    refine x.induction_on (fun _ _ ↦ ?_)
     dsimp only
     change liftOn (mk _ _) _ _ = r • (liftOn (mk _ _) _ _)
     simp_rw [RingHom.toMonoidHom_eq_coe, OneHom.toFun_eq_coe, MonoidHom.toOneHom_coe,
-      MonoidHom.coe_coe, ZeroHom.coe_mk, liftOn_mk, mul_assoc, ← smul_def]
-    rfl
+      MonoidHom.coe_coe, ZeroHom.coe_mk, liftOn_mk, mul_assoc, ← smul_def, algebraMap_smul]
 #align localized_module.div_by LocalizedModule.divBy
 
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
     divBy s (algebraMap R (Module.End R (LocalizedModule S M)) s p) = p :=
-  p.inductionOn
-    (by
-      intro ⟨m, t⟩
-      rw [Module.algebraMap_end_apply, divBy_apply]
-      erw [LocalizedModule.liftOn_mk]
-      rw [mul_assoc, ← smul_def, ZeroHom.coe_mk, RingHom.toFun_eq_coe, algebraMap_smul, smul'_mk,
-        ← Submonoid.smul_def, mk_cancel_common_right _ s]
-      rfl)
+  p.induction_on fun m t => by
+    rw [Module.algebraMap_end_apply, divBy_apply]
+    erw [smul_def]
+    rw [LocalizedModule.liftOn_mk, mul_assoc, ← smul_def, ZeroHom.coe_mk, RingHom.toFun_eq_coe,
+      algebraMap_smul, smul'_mk, ← Submonoid.smul_def, mk_cancel_common_right _ s]
 #align localized_module.div_by_mul_by LocalizedModule.divBy_mul_by
 
 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
     algebraMap R (Module.End R (LocalizedModule S M)) s (divBy s p) = p :=
-  p.inductionOn
-    (by
-      intro ⟨m, t⟩
-      rw [divBy_apply, Module.algebraMap_end_apply]
-      erw [LocalizedModule.liftOn_mk, smul'_mk]
-      rw [← Submonoid.smul_def, mk_cancel_common_right _ s]
-      rfl)
+  p.induction_on fun m t => by
+    rw [divBy_apply, Module.algebraMap_end_apply, LocalizedModule.liftOn_mk, smul'_mk,
+      ← Submonoid.smul_def, mk_cancel_common_right _ s]
 #align localized_module.mul_by_div_by LocalizedModule.mul_by_divBy
 
 end
@@ -689,12 +681,10 @@ theorem lift'_add (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
 
 theorem lift'_smul (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
     (r : R) (m) : r • LocalizedModule.lift' S g h m = LocalizedModule.lift' S g h (r • m) :=
-  m.inductionOn
-    (by
-      intro ⟨a, b⟩
-      erw [LocalizedModule.lift'_mk, LocalizedModule.smul'_mk, LocalizedModule.lift'_mk]
-      -- Porting note: We remove `generalize_proofs h1 h2`. This does nothing here.
-      erw [← map_smul, ← g.map_smul])
+  m.induction_on fun a b => by
+    rw [LocalizedModule.lift'_mk, LocalizedModule.smul'_mk, LocalizedModule.lift'_mk]
+    -- Porting note: We remove `generalize_proofs h1 h2`. This does nothing here.
+    rw [← map_smul, ← g.map_smul]
 #align localized_module.lift'_smul LocalizedModule.lift'_smul
 
 /--
@@ -754,16 +744,14 @@ instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule
         FunLike.ext _ _ <| LocalizedModule.mul_by_divBy s,
         FunLike.ext _ _ <| LocalizedModule.divBy_mul_by s⟩,
       FunLike.ext _ _ fun p =>
-        p.inductionOn <| by
+        p.induction_on <| by
           intros
           rfl⟩
   surj' p :=
-    p.inductionOn
-      (by
-        intro ⟨m, t⟩
-        refine' ⟨⟨m, t⟩, _⟩
-        erw [LocalizedModule.smul'_mk, LocalizedModule.mkLinearMap_apply, Submonoid.coe_subtype,
-          LocalizedModule.mk_cancel t])
+    p.induction_on fun m t => by
+      refine' ⟨⟨m, t⟩, _⟩
+      erw [LocalizedModule.smul'_mk, LocalizedModule.mkLinearMap_apply, Submonoid.coe_subtype,
+        LocalizedModule.mk_cancel t]
   exists_of_eq eq1 := by simpa only [eq_comm, one_smul] using LocalizedModule.mk_eq.mp eq1
 #align localized_module_is_localized_module localizedModuleIsLocalizedModule
 
@@ -780,7 +768,7 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
       rintro ⟨a, b⟩ ⟨a', b'⟩ ⟨c, eq1⟩
       dsimp
       -- Porting note: We remove `generalize_proofs h1 h2`.
-      erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← map_smul, ← map_smul,
+      rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← map_smul, ← map_smul,
         Module.End_algebraMap_isUnit_inv_apply_eq_iff', ← map_smul]
       exact (IsLocalizedModule.eq_iff_exists S f).mpr ⟨c, eq1.symm⟩)
 #align is_localized_module.from_localized_module' IsLocalizedModule.fromLocalizedModule'
@@ -799,14 +787,12 @@ theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
       intro a a' b b'
       simp only [LocalizedModule.mk_add_mk, fromLocalizedModule'_mk]
       -- Porting note: We remove `generalize_proofs h1 h2 h3`.
-      erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, smul_add, ← map_smul, ← map_smul,
+      rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, smul_add, ← map_smul, ← map_smul,
         ← map_smul, map_add]
       congr 1
       all_goals rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff']
-      · erw [mul_smul, f.map_smul]
-        rfl
-      · erw [mul_comm, f.map_smul, mul_smul]
-        rfl)
+      · simp [mul_smul, Submonoid.smul_def]
+      · rw [Submonoid.coe_mul, LinearMap.map_smul_of_tower, mul_comm, mul_smul, Submonoid.smul_def])
     x y
 #align is_localized_module.from_localized_module'_add IsLocalizedModule.fromLocalizedModule'_add
 
@@ -843,9 +829,8 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
   -- Porting note: We remove `generalize_proofs h1 h2`.
   rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← LinearMap.map_smul,
     Module.End_algebraMap_isUnit_inv_apply_eq_iff'] at eq1
-  erw [LocalizedModule.mk_eq, ← IsLocalizedModule.eq_iff_exists S f,
-    f.map_smul, f.map_smul, eq1]
-  rw [Submonoid.coe_subtype]
+  rw [LocalizedModule.mk_eq, ← IsLocalizedModule.eq_iff_exists S f, Submonoid.smul_def,
+    Submonoid.smul_def, f.map_smul, f.map_smul, eq1]
 #align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.inj
 
 theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S f := fun x =>
@@ -891,13 +876,15 @@ theorem iso_symm_apply' (m : M') (a : M) (b : S) (eq1 : b • m = f a) :
   (iso_symm_apply_aux S f m).trans <|
     LocalizedModule.mk_eq.mpr <| by
       -- Porting note: We remove `generalize_proofs h1`.
-      erw [← IsLocalizedModule.eq_iff_exists S f, f.map_smul, f.map_smul, ← (surj' _).choose_spec,
-      ← mul_smul, mul_comm, mul_smul, eq1]
+      rw [← IsLocalizedModule.eq_iff_exists S f, Submonoid.smul_def, Submonoid.smul_def, f.map_smul,
+        f.map_smul, ← (surj' _).choose_spec, ← Submonoid.smul_def, ← Submonoid.smul_def, ← mul_smul,
+        mul_comm, mul_smul, eq1]
 #align is_localized_module.iso_symm_apply' IsLocalizedModule.iso_symm_apply'
 
 theorem iso_symm_comp : (iso S f).symm.toLinearMap.comp f = LocalizedModule.mkLinearMap S M := by
-  ext m; rw [LinearMap.comp_apply, LocalizedModule.mkLinearMap_apply]
-  change (iso S f).symm _ = _; rw [iso_symm_apply']; exact one_smul _ _
+  ext m
+  rw [LinearMap.comp_apply, LocalizedModule.mkLinearMap_apply, LinearEquiv.coe_coe, iso_symm_apply']
+  exact one_smul _ _
 #align is_localized_module.iso_symm_comp IsLocalizedModule.iso_symm_comp
 
 /--
@@ -919,15 +906,14 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
     (l : M' →ₗ[R] M'') (hl : l.comp f = g) : lift S f g h = l := by
   dsimp only [IsLocalizedModule.lift]
   rw [LocalizedModule.lift_unique S g h (l.comp (iso S f).toLinearMap), LinearMap.comp_assoc,
-    show (iso S f).toLinearMap.comp (iso S f).symm.toLinearMap = LinearMap.id from _,
+    LinearEquiv.comp_coe, LinearEquiv.symm_trans_self, LinearEquiv.refl_toLinearMap,
     LinearMap.comp_id]
-  · rw [LinearEquiv.comp_toLinearMap_symm_eq, LinearMap.id_comp]
-  · rw [LinearMap.comp_assoc, ← hl]
-    congr 1
-    ext x
-    rw [LinearMap.comp_apply, LocalizedModule.mkLinearMap_apply, LinearEquiv.coe_coe, iso_apply,
-      fromLocalizedModule'_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, OneMemClass.coe_one,
-      one_smul]
+  rw [LinearMap.comp_assoc, ← hl]
+  congr 1
+  ext x
+  rw [LinearMap.comp_apply, LocalizedModule.mkLinearMap_apply, LinearEquiv.coe_coe, iso_apply,
+    fromLocalizedModule'_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, OneMemClass.coe_one,
+    one_smul]
 #align is_localized_module.lift_unique IsLocalizedModule.lift_unique
 
 /-- Universal property from localized module:
@@ -1138,8 +1124,7 @@ theorem mkOfAlgebra {R S S' : Type*} [CommRing R] [CommRing S] [CommRing S'] [Al
       exact (h₁ x x.2).mul_left_cancel e
     · intro a
       refine' ⟨((h₁ x x.2).unit⁻¹ : _) * a, _⟩
-      change (x : R) • (_ * a) = _
-      rw [Algebra.smul_def, ← mul_assoc, IsUnit.mul_val_inv, one_mul]
+      rw [Module.algebraMap_end_apply, Algebra.smul_def, ← mul_assoc, IsUnit.mul_val_inv, one_mul]
   · exact h₂
   · intros x y
     dsimp only [AlgHom.toLinearMap_apply]

Let Mₛ be a R-module and let M be a submodule of Mₛ such that Mₛ is the localization at S of M where S is a submonoid of R. Assume that Mₛ is a Rₛ-module where Rₛ is a localization of R at S. Then, any R-basis of M is a Rₛ-basis of Mₛ.

This result is used to prove the results about Basis.localizationLocalization. For that, it is necessary to move some results between files and modify some imports.

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

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

@@ -3,15 +3,16 @@ Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang, Jujian Zhang
 -/
-import Mathlib.RingTheory.IsTensorProduct
-import Mathlib.RingTheory.Localization.Module
+import Mathlib.Algebra.Algebra.Bilinear
+import Mathlib.Algebra.Algebra.RestrictScalars
+import Mathlib.RingTheory.Localization.Basic
 
 #align_import algebra.module.localized_module from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
 
 /-!
 # Localized Module
 
-Given a commutative ring `R`, a multiplicative subset `S ⊆ R` and an `R`-module `M`, we can
+Given a commutative semiring `R`, a multiplicative subset `S ⊆ R` and an `R`-module `M`, we can
 localize `M` by `S`. This gives us a `Localization S`-module.
 
 ## Main definitions
@@ -30,7 +31,6 @@ localize `M` by `S`. This gives us a `Localization S`-module.
   we have `mk r s • mk m t = mk (r • m) (s * t)` where `mk r s : Localization S` is localized ring
   by `S`.
 * `LocalizedModule.isModule` : `LocalizedModule M S` is a `Localization S`-module.
-* `IsLocalizedModule.IsBaseChange` : A localization of modules is a base change.
 
 ## Future work
 
@@ -561,7 +561,7 @@ variable (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 `IsLocalizedModule S f` describes that `f : M ⟶ M'` is the localization map identifying `M'` as
 `LocalizedModule S M`.
 -/
-class IsLocalizedModule : Prop where
+@[mk_iff] class IsLocalizedModule : Prop where
   map_units : ∀ x : S, IsUnit (algebraMap R (Module.End R M') x)
   surj' : ∀ y : M', ∃ x : M × S, x.2 • y = f x.1
   exists_of_eq : ∀ {x₁ x₂}, f x₁ = f x₂ → ∃ c : S, c • x₁ = c • x₂
@@ -581,6 +581,55 @@ lemma IsLocalizedModule.eq_iff_exists [IsLocalizedModule S f] {x₁ x₂} :
     apply_fun f at h
     simp_rw [f.map_smul_of_tower, Submonoid.smul_def, ← Module.algebraMap_end_apply R R] at h
     exact ((Module.End_isUnit_iff _).mp <| map_units f c).1 h
+
+theorem IsLocalizedModule.of_linearEquiv (e : M' ≃ₗ[R] M'') [hf : IsLocalizedModule S f] :
+    IsLocalizedModule S (e ∘ₗ f : M →ₗ[R] M'') where
+  map_units s := by
+    rw [show algebraMap R (Module.End R M'') s = e ∘ₗ (algebraMap R (Module.End R M') s) ∘ₗ e.symm
+      by ext; simp, Module.End_isUnit_iff, LinearMap.coe_comp, LinearMap.coe_comp,
+      LinearEquiv.coe_coe, LinearEquiv.coe_coe, EquivLike.comp_bijective, EquivLike.bijective_comp]
+    exact (Module.End_isUnit_iff _).mp <| hf.map_units s
+  surj' x := by
+    obtain ⟨p, h⟩ := hf.surj' (e.symm x)
+    exact ⟨p, by rw [LinearMap.coe_comp, LinearEquiv.coe_coe, Function.comp_apply, ← e.congr_arg h,
+      Submonoid.smul_def, Submonoid.smul_def, LinearEquiv.map_smul, LinearEquiv.apply_symm_apply]⟩
+  exists_of_eq h := by
+    simp_rw [LinearMap.coe_comp, LinearEquiv.coe_coe, Function.comp_apply,
+      EmbeddingLike.apply_eq_iff_eq] at h
+    exact hf.exists_of_eq h
+
+variable (M) in
+lemma isLocalizedModule_id (R') [CommSemiring R'] [Algebra R R'] [IsLocalization S R'] [Module R' M]
+    [IsScalarTower R R' M] : IsLocalizedModule S (.id : M →ₗ[R] M) where
+  map_units s := by
+    rw [← (Algebra.lsmul R (A := R') R M).commutes]; exact (IsLocalization.map_units R' s).map _
+  surj' m := ⟨(m, 1), one_smul _ _⟩
+  exists_of_eq h := ⟨1, congr_arg _ h⟩
+
+variable {S} in
+theorem isLocalizedModule_iff_isLocalization {A Aₛ} [CommSemiring A] [Algebra R A] [CommSemiring Aₛ]
+    [Algebra A Aₛ] [Algebra R Aₛ] [IsScalarTower R A Aₛ] :
+    IsLocalizedModule S (IsScalarTower.toAlgHom R A Aₛ).toLinearMap ↔
+      IsLocalization (Algebra.algebraMapSubmonoid A S) Aₛ := by
+  rw [isLocalizedModule_iff, isLocalization_iff]
+  refine and_congr ?_ (and_congr (forall_congr' fun _ ↦ ?_) (forall₂_congr fun _ _ ↦ ?_))
+  · simp_rw [← (Algebra.lmul R Aₛ).commutes, Algebra.lmul_isUnit_iff, Subtype.forall,
+      Algebra.algebraMapSubmonoid, ← SetLike.mem_coe, Submonoid.coe_map,
+      Set.ball_image_iff, ← IsScalarTower.algebraMap_apply]
+  · simp_rw [Prod.exists, Subtype.exists, Algebra.algebraMapSubmonoid]
+    simp [← IsScalarTower.algebraMap_apply, Submonoid.mk_smul, Algebra.smul_def, mul_comm]
+  · congr!; simp_rw [Subtype.exists, Algebra.algebraMapSubmonoid]; simp [Algebra.smul_def]
+
+instance {A Aₛ} [CommSemiring A] [Algebra R A][CommSemiring Aₛ] [Algebra A Aₛ] [Algebra R Aₛ]
+    [IsScalarTower R A Aₛ] [h : IsLocalization (Algebra.algebraMapSubmonoid A S) Aₛ] :
+    IsLocalizedModule S (IsScalarTower.toAlgHom R A Aₛ).toLinearMap :=
+  isLocalizedModule_iff_isLocalization.mpr h
+
+lemma isLocalizedModule_iff_isLocalization' (R') [CommSemiring R'] [Algebra R R'] :
+    IsLocalizedModule S (Algebra.ofId R R').toLinearMap ↔ IsLocalization S R' := by
+  convert isLocalizedModule_iff_isLocalization (S := S) (A := R) (Aₛ := R')
+  exact (Submonoid.map_id S).symm
+
 namespace LocalizedModule
 
 /--
@@ -1101,28 +1150,4 @@ theorem mkOfAlgebra {R S S' : Type*} [CommRing R] [CommRing S] [CommRing S'] [Al
 
 end Algebra
 
-/-- If `(f : M →ₗ[R] M')` is a localization of modules, then the map
-`(localization S) × M → N, (s, m) ↦ s • f m` is the tensor product (insomuch as it is the universal
-bilinear map).
-In particular, there is an isomorphism between `LocalizedModule S M` and `(Localization S) ⊗[R] M`
-given by `m/s ↦ (1/s) ⊗ₜ m`.
--/
-theorem isBaseChange : IsBaseChange A f := by
-  refine' IsBaseChange.of_lift_unique _ (fun Q _ _ _ _ g ↦ _)
-  have := IsLocalizedModule.is_universal S f g <| by
-    intro s
-    simp_rw [Module.End_isUnit_iff, Function.bijective_iff_existsUnique,
-      Module.algebraMap_end_apply]
-    intro q
-    refine' ⟨(IsLocalization.mk' _ 1 s : A) • q, _, _⟩
-    · simp only [← smul_assoc, IsLocalization.smul_mk'_self, map_one, one_smul]
-    · rintro q rfl
-      simp only [smul_comm _ (s : R), ← smul_assoc, IsLocalization.smul_mk'_self, map_one, one_smul]
-  rcases this with ⟨ℓ, rfl, h₂⟩
-  refine' ⟨ℓ.extendScalarsOfIsLocalization S A, by simp, fun g'' h ↦ _⟩
-  ext x
-  simp [← h₂ (LinearMap.restrictScalars R g'') h]
-
-end IsLocalizedModule
-
 end IsLocalizedModule

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -551,7 +551,11 @@ variable {R : Type*} [CommSemiring R] (S : Submonoid R)
 
 variable {M M' M'' : Type*} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid M'']
 
-variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
+variable {A : Type*} [CommSemiring A] [Algebra R A] [Module A M'] [IsLocalization S A]
+
+variable [Module R M] [Module R M'] [Module R M''] [IsScalarTower R A M']
+
+variable (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
 /-- The characteristic predicate for localized module.
 `IsLocalizedModule S f` describes that `f : M ⟶ M'` is the localization map identifying `M'` as
@@ -1045,6 +1049,14 @@ theorem mk_eq_mk' (s : S) (m : M) :
     LocalizedModule.mk_cancel, LocalizedModule.mkLinearMap_apply]
 #align is_localized_module.mk_eq_mk' IsLocalizedModule.mk_eq_mk'
 
+variable (A) in
+lemma mk'_smul_mk' (x : R) (m : M) (s t : S) :
+    IsLocalization.mk' A x s • mk' f m t = mk' f (x • m) (s * t) := by
+  apply smul_injective f (s * t)
+  conv_lhs => simp only [smul_assoc, mul_smul, smul_comm t]
+  simp only [mk'_cancel', map_smul, Submonoid.smul_def s]
+  rw [← smul_assoc, IsLocalization.smul_mk'_self, algebraMap_smul]
+
 variable (S)
 
 theorem eq_zero_iff {m : M} : f m = 0 ↔ ∃ s' : S, s' • m = 0 :=
@@ -1089,10 +1101,6 @@ theorem mkOfAlgebra {R S S' : Type*} [CommRing R] [CommRing S] [CommRing S'] [Al
 
 end Algebra
 
-variable {A : Type*}
-  [CommSemiring A] [Algebra R A] [Module A M'] [IsScalarTower R A M'] [IsLocalization S A]
-
-
 /-- If `(f : M →ₗ[R] M')` is a localization of modules, then the map
 `(localization S) × M → N, (s, m) ↦ s • f m` is the tensor product (insomuch as it is the universal
 bilinear map).

Most of the changes are minor.

Co-authored-by: Xavier Xarles <56635243+XavierXarles@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -547,7 +547,7 @@ section IsLocalizedModule
 
 universe u v
 
-variable {R : Type*} [CommRing R] (S : Submonoid R)
+variable {R : Type*} [CommSemiring R] (S : Submonoid R)
 
 variable {M M' M'' : Type*} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid M'']
 
@@ -1090,7 +1090,7 @@ theorem mkOfAlgebra {R S S' : Type*} [CommRing R] [CommRing S] [CommRing S'] [Al
 end Algebra
 
 variable {A : Type*}
-  [CommRing A] [Algebra R A] [Module A M'] [IsScalarTower R A M'] [IsLocalization S A]
+  [CommSemiring A] [Algebra R A] [Module A M'] [IsScalarTower R A M'] [IsLocalization S A]
 
 
 /-- If `(f : M →ₗ[R] M')` is a localization of modules, then the map

The construction of LocalizedModule is done using IsLocalization rather than Localization. The corresponding instances for Localization are deduced automatically by Lean. One drawback is that many instances are now marked noncomputable.

@@ -3,11 +3,8 @@ Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang, Jujian Zhang
 -/
-import Mathlib.GroupTheory.MonoidLocalization
-import Mathlib.RingTheory.Localization.Basic
-import Mathlib.RingTheory.Localization.Module
-import Mathlib.Algebra.Algebra.RestrictScalars
 import Mathlib.RingTheory.IsTensorProduct
+import Mathlib.RingTheory.Localization.Module
 
 #align_import algebra.module.localized_module from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
 
@@ -49,6 +46,8 @@ variable {R : Type u} [CommSemiring R] (S : Submonoid R)
 
 variable (M : Type v) [AddCommMonoid M] [Module R M]
 
+variable (T : Type*) [CommSemiring T] [Algebra R T] [IsLocalization S T]
+
 /-- The equivalence relation on `M × S` where `(m1, s1) ≈ (m2, s2)` if and only if
 for some (u : S), u * (s2 • m1 - s1 • m2) = 0-/
 /- Porting note: We use small letter `r` since `R` is used for a ring. -/
@@ -318,90 +317,88 @@ theorem mk_mul_mk {A : Type*} [Semiring A] [Algebra R A] {a₁ a₂ : A} {s₁ s
   rfl
 #align localized_module.mk_mul_mk LocalizedModule.mk_mul_mk
 
-instance : SMul (Localization S) (LocalizedModule S M) where
-  smul f x :=
-    (Localization.liftOn f
-      (fun r s =>
-        (liftOn x (fun p => (mk (r • p.1) (s * p.2)))
-          (by
-            rintro ⟨m1, t1⟩ ⟨m2, t2⟩ ⟨u, h⟩
-            refine' mk_eq.mpr ⟨u, _⟩
-            have h' := congr_arg ((s • r) • ·) h
-            simp only [← mul_smul, smul_eq_mul, mul_comm, mul_left_comm, Submonoid.smul_def,
-              Submonoid.coe_mul] at h' ⊢
-            rw [h'])))
+noncomputable instance : SMul T (LocalizedModule S M) where
+  smul x p :=
+    let a := IsLocalization.sec S x
+    liftOn p (fun p ↦ mk (a.1 • p.1) (a.2 * p.2))
       (by
-        induction' x using LocalizedModule.induction_on with m t
-        rintro r r' s s' h
-        simp only [liftOn_mk, liftOn_mk, mk_eq]
-        obtain ⟨u, eq1⟩ := Localization.r_iff_exists.mp h
-        use u
-        have eq1' := congr_arg (· • t • m) eq1
-        simp only [← mul_smul, smul_assoc, Submonoid.smul_def, Submonoid.coe_mul] at eq1' ⊢
-        ring_nf at eq1' ⊢
-        rw [eq1']))
+        rintro p p' ⟨s, h⟩
+        refine mk_eq.mpr ⟨s, ?_⟩
+        calc
+          _ = a.2 • a.1 • s • p'.2 • p.1 := by
+            simp_rw [Submonoid.smul_def, Submonoid.coe_mul, ← mul_smul]; ring_nf
+          _ = a.2 • a.1 • s • p.2 • p'.1 := by rw [h]
+          _ = s • (a.2 * p.2) • a.1 • p'.1 := by
+            simp_rw [Submonoid.smul_def, ← mul_smul, Submonoid.coe_mul]; ring_nf )
+
+theorem smul_def (x : T) (m : M) (s : S) :
+    x • mk m s = mk ((IsLocalization.sec S x).1 • m) ((IsLocalization.sec S x).2 * s) := rfl
+
+theorem mk'_smul_mk (r : R) (m : M) (s s' : S) :
+    IsLocalization.mk' T r s • mk m s' = mk (r • m) (s * s') := by
+  rw [smul_def, mk_eq]
+  obtain ⟨c, hc⟩ := IsLocalization.eq.mp <| IsLocalization.mk'_sec T (IsLocalization.mk' T r s)
+  use c
+  simp_rw [← mul_smul, Submonoid.smul_def, Submonoid.coe_mul, ← mul_smul, ← mul_assoc,
+    mul_comm _ (s':R), mul_assoc, hc]
 
 theorem mk_smul_mk (r : R) (m : M) (s t : S) :
     Localization.mk r s • mk m t = mk (r • m) (s * t) := by
-  dsimp only [HSMul.hSMul, SMul.smul]
-  rw [Localization.liftOn_mk, liftOn_mk]
+  rw [Localization.mk_eq_mk']
+  exact mk'_smul_mk ..
 #align localized_module.mk_smul_mk LocalizedModule.mk_smul_mk
 
-private theorem one_smul' (m : LocalizedModule S M) : (1 : Localization S) • m = m := by
-  induction' m using LocalizedModule.induction_on with m s
-  rw [← Localization.mk_one, mk_smul_mk, one_smul, one_mul]
-
-private theorem mul_smul' (x y : Localization S) (m : LocalizedModule S M) :
-    (x * y) • m = x • y • m := by
-  induction' x using Localization.induction_on with data
-  induction' y using Localization.induction_on with data'
-  rcases data, data' with ⟨⟨r, s⟩, ⟨r', s'⟩⟩
-  induction' m using LocalizedModule.induction_on with m t
-  rw [Localization.mk_mul, mk_smul_mk, mk_smul_mk, mk_smul_mk, mul_smul, mul_assoc]
-
-private theorem smul_add' (x : Localization S) (y z : LocalizedModule S M) :
-    x • (y + z) = x • y + x • z := by
-  induction' x using Localization.induction_on with data
-  rcases data with ⟨r, u⟩
-  induction' y using LocalizedModule.induction_on with m s
-  induction' z using LocalizedModule.induction_on with n t
-  rw [mk_smul_mk, mk_smul_mk, mk_add_mk, mk_smul_mk, mk_add_mk, mk_eq]
-  use 1
-  simp only [one_smul, smul_add, ← mul_smul, Submonoid.smul_def, Submonoid.coe_mul]
-  ring_nf
-
-private theorem smul_zero' (x : Localization S) : x • (0 : LocalizedModule S M) = 0 := by
-  induction' x using Localization.induction_on with data
-  rcases data with ⟨r, s⟩
-  rw [← zero_mk s, mk_smul_mk, smul_zero, zero_mk, zero_mk]
-
-private theorem add_smul' (x y : Localization S) (z : LocalizedModule S M) :
-    (x + y) • z = x • z + y • z := by
-  induction' x using Localization.induction_on with datax
-  induction' y using Localization.induction_on with datay
-  induction' z using LocalizedModule.induction_on with m t
-  rcases datax, datay with ⟨⟨r, s⟩, ⟨r', s'⟩⟩
-  rw [Localization.add_mk, mk_smul_mk, mk_smul_mk, mk_smul_mk, mk_add_mk, mk_eq]
-  use 1
-  simp only [one_smul, add_smul, smul_add, ← mul_smul, Submonoid.smul_def, Submonoid.coe_mul,
-    Submonoid.coe_one]
-  rw [add_comm]
-  -- Commutativity of addition in the module is not applied by `Ring`.
-  ring_nf
-
-private theorem zero_smul' (x : LocalizedModule S M) : (0 : Localization S) • x = 0 := by
-  induction' x using LocalizedModule.induction_on with m s
-  rw [← Localization.mk_zero s, mk_smul_mk, zero_smul, zero_mk]
-
-instance isModule : Module (Localization S) (LocalizedModule S M) where
+variable {T}
+
+private theorem one_smul_aux (p : LocalizedModule S M) : (1 : T) • p = p := by
+  induction' p using LocalizedModule.induction_on with m s
+  rw [show (1:T) = IsLocalization.mk' T (1:R) (1:S) by rw [IsLocalization.mk'_one, map_one]]
+  rw [mk'_smul_mk, one_smul, one_mul]
+
+private theorem mul_smul_aux (x y : T) (p : LocalizedModule S M) :
+    (x * y) • p = x • y • p := by
+  induction' p using LocalizedModule.induction_on with m s
+  rw [← IsLocalization.mk'_sec (M := S) T x, ← IsLocalization.mk'_sec (M := S) T y]
+  simp_rw [← IsLocalization.mk'_mul, mk'_smul_mk, ← mul_smul, mul_assoc]
+
+private theorem smul_add_aux (x : T) (p q : LocalizedModule S M) :
+    x • (p + q) = x • p + x • q := by
+  induction' p using LocalizedModule.induction_on with m s
+  induction' q using LocalizedModule.induction_on with n t
+  rw [smul_def, smul_def, mk_add_mk, mk_add_mk]
+  rw [show x • _ =  IsLocalization.mk' T _ _ • _ by rw [IsLocalization.mk'_sec (M := S) T]]
+  rw [← IsLocalization.mk'_cancel _ _ (IsLocalization.sec S x).2, mk'_smul_mk]
+  congr 1
+  · simp only [Submonoid.smul_def, smul_add, ← mul_smul, Submonoid.coe_mul]; ring_nf
+  · rw [mul_mul_mul_comm] -- ring does not work here
+
+private theorem smul_zero_aux (x : T) : x • (0 : LocalizedModule S M) = 0 := by
+  erw [smul_def, smul_zero, zero_mk]
+
+private theorem add_smul_aux (x y : T) (p : LocalizedModule S M) :
+    (x + y) • p = x • p + y • p := by
+  induction' p using LocalizedModule.induction_on with m s
+  rw [smul_def T x, smul_def T y, mk_add_mk, show (x + y) • _ =  IsLocalization.mk' T _ _ • _ by
+    rw [← IsLocalization.mk'_sec (M := S) T x, ← IsLocalization.mk'_sec (M := S) T y,
+      ← IsLocalization.mk'_add, IsLocalization.mk'_cancel _ _ s], mk'_smul_mk, ← smul_assoc,
+    ← smul_assoc, ← add_smul]
+  congr 1
+  · simp only [Submonoid.smul_def, Submonoid.coe_mul, smul_eq_mul]; ring_nf
+  · rw [mul_mul_mul_comm, mul_assoc] -- ring does not work here
+
+private theorem zero_smul_aux (p : LocalizedModule S M) : (0 : T) • p = 0 := by
+  induction' p using LocalizedModule.induction_on with m s
+  rw [show (0:T) = IsLocalization.mk' T (0:R) (1:S) by rw [IsLocalization.mk'_zero], mk'_smul_mk,
+    zero_smul, zero_mk]
+
+noncomputable instance isModule : Module T (LocalizedModule S M) where
   smul := (· • ·)
-  one_smul := one_smul'
-  mul_smul := mul_smul'
-  smul_add := smul_add'
-  smul_zero := smul_zero'
-  add_smul := add_smul'
-  zero_smul := zero_smul'
-#align localized_module.is_module LocalizedModule.isModule
+  one_smul := one_smul_aux
+  mul_smul := mul_smul_aux
+  smul_add := smul_add_aux
+  smul_zero := smul_zero_aux
+  add_smul := add_smul_aux
+  zero_smul := zero_smul_aux
 
 @[simp]
 theorem mk_cancel_common_left (s' s : S) (m : M) : mk (s' • m) (s' * s) = mk m s :=
@@ -421,7 +418,7 @@ theorem mk_cancel_common_right (s s' : S) (m : M) : mk (s' • m) (s * s') = mk
   mk_eq.mpr ⟨1, by simp [mul_smul]⟩
 #align localized_module.mk_cancel_common_right LocalizedModule.mk_cancel_common_right
 
-instance isModule' : Module R (LocalizedModule S M) :=
+noncomputable instance isModule' : Module R (LocalizedModule S M) :=
   { Module.compHom (LocalizedModule S M) <| algebraMap R (Localization S) with }
 #align localized_module.is_module' LocalizedModule.isModule'
 
@@ -429,35 +426,43 @@ theorem smul'_mk (r : R) (s : S) (m : M) : r • mk m s = mk (r • m) s := by
   erw [mk_smul_mk r m 1 s, one_mul]
 #align localized_module.smul'_mk LocalizedModule.smul'_mk
 
-instance {A : Type*} [Semiring A] [Algebra R A] :
-    Algebra (Localization S) (LocalizedModule S A) :=
-  Algebra.ofModule
-    (by
-      intro r x₁ x₂
-      obtain ⟨y, s, rfl : IsLocalization.mk' _ y s = r⟩ := IsLocalization.mk'_surjective S r
-      obtain ⟨⟨a₁, s₁⟩, rfl : mk a₁ s₁ = x₁⟩ := Quotient.exists_rep x₁
-      obtain ⟨⟨a₂, s₂⟩, rfl : mk a₂ s₂ = x₂⟩ := Quotient.exists_rep x₂
-      rw [mk_mul_mk, ← Localization.mk_eq_mk', mk_smul_mk, mk_smul_mk, mk_mul_mk, mul_assoc,
-        smul_mul_assoc])
-    (by
-      intro r x₁ x₂
-      obtain ⟨y, s, rfl : IsLocalization.mk' _ y s = r⟩ := IsLocalization.mk'_surjective S r
-      obtain ⟨⟨a₁, s₁⟩, rfl : mk a₁ s₁ = x₁⟩ := Quotient.exists_rep x₁
-      obtain ⟨⟨a₂, s₂⟩, rfl : mk a₂ s₂ = x₂⟩ := Quotient.exists_rep x₂
-      rw [mk_mul_mk, ← Localization.mk_eq_mk', mk_smul_mk, mk_smul_mk, mk_mul_mk, mul_left_comm,
-        mul_smul_comm])
+theorem smul'_mul {A : Type*} [Semiring A] [Algebra R A] (x : T) (p₁ p₂ : LocalizedModule S A) :
+    x • p₁ * p₂ = x • (p₁ * p₂) := by
+  obtain ⟨⟨a₁, s₁⟩, rfl : mk a₁ s₁ = p₁⟩ := Quotient.exists_rep p₁
+  obtain ⟨⟨a₂, s₂⟩, rfl : mk a₂ s₂ = p₂⟩ := Quotient.exists_rep p₂
+  rw [mk_mul_mk, smul_def, smul_def, mk_mul_mk, mul_assoc, smul_mul_assoc]
 
-theorem algebraMap_mk {A : Type*} [Semiring A] [Algebra R A] (a : R) (s : S) :
-    algebraMap _ _ (Localization.mk a s) = mk (algebraMap R A a) s := by
+theorem mul_smul' {A : Type*} [Semiring A] [Algebra R A] (x : T) (p₁ p₂ : LocalizedModule S A) :
+    p₁ * x • p₂ = x • (p₁ * p₂) := by
+  obtain ⟨⟨a₁, s₁⟩, rfl : mk a₁ s₁ = p₁⟩ := Quotient.exists_rep p₁
+  obtain ⟨⟨a₂, s₂⟩, rfl : mk a₂ s₂ = p₂⟩ := Quotient.exists_rep p₂
+  rw [smul_def, mk_mul_mk, mk_mul_mk, smul_def, mul_left_comm, mul_smul_comm]
+
+variable (T)
+
+noncomputable instance {A : Type*} [Semiring A] [Algebra R A] : Algebra T (LocalizedModule S A) :=
+  Algebra.ofModule smul'_mul mul_smul'
+
+theorem algebraMap_mk' {A : Type*} [Semiring A] [Algebra R A] (a : R) (s : S) :
+    algebraMap _ _ (IsLocalization.mk' T a s) = mk (algebraMap R A a) s := by
   rw [Algebra.algebraMap_eq_smul_one]
   change _ • mk _ _ = _
-  rw [mk_smul_mk, Algebra.algebraMap_eq_smul_one, mul_one]
+  rw [mk'_smul_mk, Algebra.algebraMap_eq_smul_one, mul_one]
+
+theorem algebraMap_mk {A : Type*} [Semiring A] [Algebra R A] (a : R) (s : S) :
+    algebraMap _ _ (Localization.mk a s) = mk (algebraMap R A a) s := by
+  rw [Localization.mk_eq_mk']
+  exact algebraMap_mk' ..
 #align localized_module.algebra_map_mk LocalizedModule.algebraMap_mk
 
-instance : IsScalarTower R (Localization S) (LocalizedModule S M) :=
-  RestrictScalars.isScalarTower R (Localization S) (LocalizedModule S M)
+instance : IsScalarTower R T (LocalizedModule S M) where
+  smul_assoc r x p := by
+    induction' p using LocalizedModule.induction_on with m s
+    rw [← IsLocalization.mk'_sec (M := S) T x, IsLocalization.smul_mk', mk'_smul_mk, mk'_smul_mk,
+      smul'_mk, mul_smul]
 
-instance algebra' {A : Type*} [Semiring A] [Algebra R A] : Algebra R (LocalizedModule S A) :=
+noncomputable instance algebra' {A : Type*} [Semiring A] [Algebra R A] :
+    Algebra R (LocalizedModule S A) :=
   { (algebraMap (Localization S) (LocalizedModule S A)).comp (algebraMap R <| Localization S),
     show Module R (LocalizedModule S A) by infer_instance with
     commutes' := by
@@ -494,25 +499,21 @@ end
 @[simps]
 def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M where
   toFun p :=
-    p.liftOn (fun p => mk p.1 (s * p.2)) fun ⟨a, b⟩ ⟨a', b'⟩ ⟨c, eq1⟩ =>
-      mk_eq.mpr ⟨c, by rw [mul_smul, mul_smul, smul_comm c, eq1, smul_comm s]⟩
-  map_add' x y :=
-    x.induction_on₂
-      (by
-        intro m₁ m₂ t₁ t₂
-        simp only [mk_add_mk, LocalizedModule.liftOn_mk, mul_smul, ← smul_add, mul_assoc,
-          mk_cancel_common_left s]
-        rw [show s * (t₁ * t₂) = t₁ * (s * t₂) by
-            ext
-            simp only [Submonoid.coe_mul]
-            ring])
-      y
-  map_smul' r x :=
-    x.inductionOn <| by
-      intro
-      dsimp only
-      change liftOn (mk _ _) _ _ = r • (liftOn (mk _ _) _ _)
-      simp [LocalizedModule.liftOn_mk, smul'_mk]
+    p.liftOn (fun p => mk p.1 (p.2 * s)) fun ⟨a, b⟩ ⟨a', b'⟩ ⟨c, eq1⟩ =>
+      mk_eq.mpr ⟨c, by rw [mul_smul, mul_smul, smul_comm _ s, smul_comm _ s, eq1, smul_comm _ s,
+        smul_comm _ s]⟩
+  map_add' x y := by
+    refine x.induction_on₂ ?_ y
+    intro m₁ m₂ t₁ t₂
+    simp_rw [mk_add_mk, LocalizedModule.liftOn_mk, mk_add_mk, mul_smul, mul_comm _ s, mul_assoc,
+      smul_comm _ s, ← smul_add, mul_left_comm s t₁ t₂, mk_cancel_common_left s]
+  map_smul' r x := by
+    refine x.inductionOn (fun _ ↦ ?_)
+    dsimp only
+    change liftOn (mk _ _) _ _ = r • (liftOn (mk _ _) _ _)
+    simp_rw [RingHom.toMonoidHom_eq_coe, OneHom.toFun_eq_coe, MonoidHom.toOneHom_coe,
+      MonoidHom.coe_coe, ZeroHom.coe_mk, liftOn_mk, mul_assoc, ← smul_def]
+    rfl
 #align localized_module.div_by LocalizedModule.divBy
 
 theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
@@ -520,11 +521,11 @@ theorem divBy_mul_by (s : S) (p : LocalizedModule S M) :
   p.inductionOn
     (by
       intro ⟨m, t⟩
-      simp only [Module.algebraMap_end_apply, smul'_mk, divBy_apply]
+      rw [Module.algebraMap_end_apply, divBy_apply]
       erw [LocalizedModule.liftOn_mk]
-      simp only [one_mul]
-      change mk (s • m) (s * t) = mk m t
-      rw [mk_cancel_common_left s t])
+      rw [mul_assoc, ← smul_def, ZeroHom.coe_mk, RingHom.toFun_eq_coe, algebraMap_smul, smul'_mk,
+        ← Submonoid.smul_def, mk_cancel_common_right _ s]
+      rfl)
 #align localized_module.div_by_mul_by LocalizedModule.divBy_mul_by
 
 theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
@@ -532,10 +533,10 @@ theorem mul_by_divBy (s : S) (p : LocalizedModule S M) :
   p.inductionOn
     (by
       intro ⟨m, t⟩
-      simp only [LocalizedModule.liftOn_mk, divBy_apply, Module.algebraMap_end_apply, smul'_mk]
+      rw [divBy_apply, Module.algebraMap_end_apply]
       erw [LocalizedModule.liftOn_mk, smul'_mk]
-      change mk (s • m) (s * t) = mk m t
-      rw [mk_cancel_common_left s t])
+      rw [← Submonoid.smul_def, mk_cancel_common_right _ s]
+      rfl)
 #align localized_module.mul_by_div_by LocalizedModule.mul_by_divBy
 
 end

@@ -142,6 +142,12 @@ theorem liftOn₂_mk {α : Type*} (f : M × S → M × S → α)
 instance : Zero (LocalizedModule S M) :=
   ⟨mk 0 1⟩
 
+/-- If `S` contains `0` then the localization at `S` is trivial. -/
+theorem subsingleton (h : 0 ∈ S) : Subsingleton (LocalizedModule S M) := by
+  refine ⟨fun a b ↦ ?_⟩
+  induction a,b using LocalizedModule.induction_on₂
+  exact mk_eq.mpr ⟨⟨0, h⟩, by simp only [Submonoid.mk_smul, zero_smul]⟩
+
 @[simp]
 theorem zero_mk (s : S) : mk (0 : M) s = 0 :=
   mk_eq.mpr ⟨1, by rw [one_smul, smul_zero, smul_zero, one_smul]⟩

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

@@ -61,8 +61,8 @@ theorem r.isEquiv : IsEquiv _ (r S M) :=
     trans := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨m3, s3⟩ ⟨u1, hu1⟩ ⟨u2, hu2⟩ => by
       use u1 * u2 * s2
       -- Put everything in the same shape, sorting the terms using `simp`
-      have hu1' := congr_arg ((· • ·) (u2 * s3)) hu1.symm
-      have hu2' := congr_arg ((· • ·) (u1 * s1)) hu2.symm
+      have hu1' := congr_arg ((u2 * s3) • ·) hu1.symm
+      have hu2' := congr_arg ((u1 * s1) • ·) hu2.symm
       simp only [← mul_smul, smul_assoc, mul_assoc, mul_comm, mul_left_comm] at hu1' hu2' ⊢
       rw [hu2', hu1']
     symm := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => ⟨u, hu.symm⟩ }
@@ -154,8 +154,8 @@ instance : Add (LocalizedModule S M) where
           mk_eq.mpr
             ⟨u1 * u2, by
               -- Put everything in the same shape, sorting the terms using `simp`
-              have hu1' := congr_arg ((· • ·) (u2 * s2 * s2')) hu1
-              have hu2' := congr_arg ((· • ·) (u1 * s1 * s1')) hu2
+              have hu1' := congr_arg ((u2 * s2 * s2') • ·) hu1
+              have hu2' := congr_arg ((u1 * s1 * s1') • ·) hu2
               simp only [smul_add, ← mul_smul, smul_assoc, mul_assoc, mul_comm,
                 mul_left_comm] at hu1' hu2' ⊢
               rw [hu1', hu2']⟩
@@ -320,7 +320,7 @@ instance : SMul (Localization S) (LocalizedModule S M) where
           (by
             rintro ⟨m1, t1⟩ ⟨m2, t2⟩ ⟨u, h⟩
             refine' mk_eq.mpr ⟨u, _⟩
-            have h' := congr_arg ((· • ·) (s • r)) h
+            have h' := congr_arg ((s • r) • ·) h
             simp only [← mul_smul, smul_eq_mul, mul_comm, mul_left_comm, Submonoid.smul_def,
               Submonoid.coe_mul] at h' ⊢
             rw [h'])))

I think these are all positive or neutral in isolation, and they avoid breakages from a more interesting PR (providing a @[csimp] lemma for npowRec).

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -237,11 +237,9 @@ theorem mk_neg {M : Type*} [AddCommGroup M] [Module R M] {m : M} {s : S} : mk (-
   rfl
 #align localized_module.mk_neg LocalizedModule.mk_neg
 
-set_option maxHeartbeats 500000 in
 instance {A : Type*} [Semiring A] [Algebra R A] {S : Submonoid R} :
-    Semiring (LocalizedModule S A) :=
-  { show (AddCommMonoid (LocalizedModule S A)) by infer_instance with
-    mul := fun m₁ m₂ =>
+    Monoid (LocalizedModule S A) :=
+  { mul := fun m₁ m₂ =>
       liftOn₂ m₁ m₂ (fun x₁ x₂ => LocalizedModule.mk (x₁.1 * x₂.1) (x₁.2 * x₂.2))
         (by
           rintro ⟨a₁, s₁⟩ ⟨a₂, s₂⟩ ⟨b₁, t₁⟩ ⟨b₂, t₂⟩ ⟨u₁, e₁⟩ ⟨u₂, e₂⟩
@@ -254,6 +252,23 @@ instance {A : Type*} [Semiring A] [Algebra R A] {S : Submonoid R} :
           all_goals
             rw [smul_smul, mul_mul_mul_comm, ← smul_eq_mul, ← smul_eq_mul A, smul_smul_smul_comm,
               mul_smul, mul_smul])
+    one := mk 1 (1 : S)
+    one_mul := by
+      rintro ⟨a, s⟩
+      exact mk_eq.mpr ⟨1, by simp only [one_mul, one_smul]⟩
+    mul_one := by
+      rintro ⟨a, s⟩
+      exact mk_eq.mpr ⟨1, by simp only [mul_one, one_smul]⟩
+    mul_assoc := by
+      rintro ⟨a₁, s₁⟩ ⟨a₂, s₂⟩ ⟨a₃, s₃⟩
+      apply mk_eq.mpr _
+      use 1
+      simp only [one_mul, smul_smul, ← mul_assoc, mul_right_comm] }
+
+instance {A : Type*} [Semiring A] [Algebra R A] {S : Submonoid R} :
+    Semiring (LocalizedModule S A) :=
+  { show (AddCommMonoid (LocalizedModule S A)) by infer_instance,
+    show (Monoid (LocalizedModule S A)) by infer_instance with
     left_distrib := by
       rintro ⟨a₁, s₁⟩ ⟨a₂, s₂⟩ ⟨a₃, s₃⟩
       apply mk_eq.mpr _
@@ -271,19 +286,7 @@ instance {A : Type*} [Semiring A] [Algebra R A] {S : Submonoid R} :
       exact mk_eq.mpr ⟨1, by simp only [zero_mul, smul_zero]⟩
     mul_zero := by
       rintro ⟨a, s⟩
-      exact mk_eq.mpr ⟨1, by simp only [mul_zero, smul_zero]⟩
-    mul_assoc := by
-      rintro ⟨a₁, s₁⟩ ⟨a₂, s₂⟩ ⟨a₃, s₃⟩
-      apply mk_eq.mpr _
-      use 1
-      simp only [one_mul, smul_smul, ← mul_assoc, mul_right_comm]
-    one := mk 1 (1 : S)
-    one_mul := by
-      rintro ⟨a, s⟩
-      exact mk_eq.mpr ⟨1, by simp only [one_mul, one_smul]⟩
-    mul_one := by
-      rintro ⟨a, s⟩
-      exact mk_eq.mpr ⟨1, by simp only [mul_one, one_smul]⟩ }
+      exact mk_eq.mpr ⟨1, by simp only [mul_zero, smul_zero]⟩ }
 
 instance {A : Type*} [CommSemiring A] [Algebra R A] {S : Submonoid R} :
     CommSemiring (LocalizedModule S A) :=

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -717,8 +717,8 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
       rintro ⟨a, b⟩ ⟨a', b'⟩ ⟨c, eq1⟩
       dsimp
       -- Porting note: We remove `generalize_proofs h1 h2`.
-      erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ←map_smul, ←map_smul,
-        Module.End_algebraMap_isUnit_inv_apply_eq_iff', ←map_smul]
+      erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← map_smul, ← map_smul,
+        Module.End_algebraMap_isUnit_inv_apply_eq_iff', ← map_smul]
       exact (IsLocalizedModule.eq_iff_exists S f).mpr ⟨c, eq1.symm⟩)
 #align is_localized_module.from_localized_module' IsLocalizedModule.fromLocalizedModule'
 
@@ -736,8 +736,8 @@ theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
       intro a a' b b'
       simp only [LocalizedModule.mk_add_mk, fromLocalizedModule'_mk]
       -- Porting note: We remove `generalize_proofs h1 h2 h3`.
-      erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, smul_add, ←map_smul, ←map_smul,
-        ←map_smul, map_add]
+      erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, smul_add, ← map_smul, ← map_smul,
+        ← map_smul, map_add]
       congr 1
       all_goals rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff']
       · erw [mul_smul, f.map_smul]

The other direction is a consequence of IsLocalization.map_units.

Also do the same for LocalizationMap and IsLocalizedModule.

This means we have one less fact to prove when constructing an IsLocalization (etc.) instance (thus many proofs are golfed), but once we construct it we still have access to the eq_iff_exists lemmas (without the prime) so the API doesn't get less powerful.

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

@@ -550,11 +550,11 @@ variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M 
 class IsLocalizedModule : Prop where
   map_units : ∀ x : S, IsUnit (algebraMap R (Module.End R M') x)
   surj' : ∀ y : M', ∃ x : M × S, x.2 • y = f x.1
-  eq_iff_exists' : ∀ {x₁ x₂}, f x₁ = f x₂ ↔ ∃ c : S, c • x₂ = c • x₁
+  exists_of_eq : ∀ {x₁ x₂}, f x₁ = f x₂ → ∃ c : S, c • x₁ = c • x₂
 #align is_localized_module IsLocalizedModule
 
 attribute [nolint docBlame] IsLocalizedModule.map_units IsLocalizedModule.surj'
-  IsLocalizedModule.eq_iff_exists'
+  IsLocalizedModule.exists_of_eq
 
 -- Porting note: Manually added to make `S` and `f` explicit.
 lemma IsLocalizedModule.surj [IsLocalizedModule S f] (y : M') : ∃ x : M × S, x.2 • y = f x.1 :=
@@ -562,9 +562,11 @@ lemma IsLocalizedModule.surj [IsLocalizedModule S f] (y : M') : ∃ x : M × S,
 
 -- Porting note: Manually added to make `S` and `f` explicit.
 lemma IsLocalizedModule.eq_iff_exists [IsLocalizedModule S f] {x₁ x₂} :
-    f x₁ = f x₂ ↔ ∃ c : S, c • x₂ = c • x₁ :=
-eq_iff_exists'
-
+    f x₁ = f x₂ ↔ ∃ c : S, c • x₁ = c • x₂ :=
+  Iff.intro exists_of_eq fun ⟨c, h⟩ ↦ by
+    apply_fun f at h
+    simp_rw [f.map_smul_of_tower, Submonoid.smul_def, ← Module.algebraMap_end_apply R R] at h
+    exact ((Module.End_isUnit_iff _).mp <| map_units f c).1 h
 namespace LocalizedModule
 
 /--
@@ -699,10 +701,7 @@ instance localizedModuleIsLocalizedModule : IsLocalizedModule S (LocalizedModule
         refine' ⟨⟨m, t⟩, _⟩
         erw [LocalizedModule.smul'_mk, LocalizedModule.mkLinearMap_apply, Submonoid.coe_subtype,
           LocalizedModule.mk_cancel t])
-  eq_iff_exists' :=
-    { mp := fun eq1 => by simpa only [eq_comm, one_smul] using LocalizedModule.mk_eq.mp eq1
-      mpr := fun ⟨c, eq1⟩ =>
-        LocalizedModule.mk_eq.mpr ⟨c, by simpa only [eq_comm, one_smul] using eq1⟩ }
+  exists_of_eq eq1 := by simpa only [eq_comm, one_smul] using LocalizedModule.mk_eq.mp eq1
 #align localized_module_is_localized_module localizedModuleIsLocalizedModule
 
 namespace IsLocalizedModule
@@ -720,7 +719,7 @@ noncomputable def fromLocalizedModule' : LocalizedModule S M → M' := fun p =>
       -- Porting note: We remove `generalize_proofs h1 h2`.
       erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ←map_smul, ←map_smul,
         Module.End_algebraMap_isUnit_inv_apply_eq_iff', ←map_smul]
-      exact (IsLocalizedModule.eq_iff_exists S f).mpr ⟨c, eq1⟩)
+      exact (IsLocalizedModule.eq_iff_exists S f).mpr ⟨c, eq1.symm⟩)
 #align is_localized_module.from_localized_module' IsLocalizedModule.fromLocalizedModule'
 
 @[simp]
@@ -1071,10 +1070,11 @@ theorem mkOfAlgebra {R S S' : Type*} [CommRing R] [CommRing S] [CommRing S'] [Al
       change (x : R) • (_ * a) = _
       rw [Algebra.smul_def, ← mul_assoc, IsUnit.mul_val_inv, one_mul]
   · exact h₂
-  · intros
+  · intros x y
     dsimp only [AlgHom.toLinearMap_apply]
-    rw [eq_comm, ← sub_eq_zero, ← map_sub, h₃]
+    rw [← sub_eq_zero, ← map_sub, h₃]
     simp_rw [smul_sub, sub_eq_zero]
+    exact id
 #align is_localized_module.mk_of_algebra IsLocalizedModule.mkOfAlgebra
 
 end Algebra

We have turned to Type* instead of Type _, but many of them remained in mathlib because the straight replacement did not work. In general, having Type _ before the colon is a code smell, though, as it hides which types should be in the same universe and which shouldn't, and is not very robust.

This PR replaces most of the remaining Type _ before the colon (except those in category theory) by Type* or Type u. This has uncovered a few bugs (where declarations were not as polymorphic as they should be).

I had to increase heartbeats at two places when replacing Type _ by Type*, but I think it's worth it as it's really more robust.

@@ -237,8 +237,8 @@ theorem mk_neg {M : Type*} [AddCommGroup M] [Module R M] {m : M} {s : S} : mk (-
   rfl
 #align localized_module.mk_neg LocalizedModule.mk_neg
 
-set_option maxHeartbeats 400000 in
-instance {A : Type _} [Semiring A] [Algebra R A] {S : Submonoid R} :
+set_option maxHeartbeats 500000 in
+instance {A : Type*} [Semiring A] [Algebra R A] {S : Submonoid R} :
     Semiring (LocalizedModule S A) :=
   { show (AddCommMonoid (LocalizedModule S A)) by infer_instance with
     mul := fun m₁ m₂ =>
@@ -292,12 +292,12 @@ instance {A : Type*} [CommSemiring A] [Algebra R A] {S : Submonoid R} :
       rintro ⟨a₁, s₁⟩ ⟨a₂, s₂⟩
       exact mk_eq.mpr ⟨1, by simp only [one_smul, mul_comm]⟩ }
 
-instance {A : Type} [Ring A] [Algebra R A] {S : Submonoid R} :
+instance {A : Type*} [Ring A] [Algebra R A] {S : Submonoid R} :
     Ring (LocalizedModule S A) :=
   { inferInstanceAs (AddCommGroup (LocalizedModule S A)),
     inferInstanceAs (Semiring (LocalizedModule S A)) with }
 
-instance {A : Type _} [CommRing A] [Algebra R A] {S : Submonoid R} :
+instance {A : Type*} [CommRing A] [Algebra R A] {S : Submonoid R} :
     CommRing (LocalizedModule S A) :=
   { show (Ring (LocalizedModule S A)) by infer_instance with
     mul_comm := by

@@ -147,8 +147,8 @@ theorem zero_mk (s : S) : mk (0 : M) s = 0 :=
   mk_eq.mpr ⟨1, by rw [one_smul, smul_zero, smul_zero, one_smul]⟩
 #align localized_module.zero_mk LocalizedModule.zero_mk
 
-instance : Add (LocalizedModule S M)
-    where add p1 p2 :=
+instance : Add (LocalizedModule S M) where
+  add p1 p2 :=
     liftOn₂ p1 p2 (fun x y => mk (y.2 • x.1 + x.2 • y.1) (x.2 * y.2)) <|
       fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨m1', s1'⟩ ⟨m2', s2'⟩ ⟨u1, hu1⟩ ⟨u2, hu2⟩ =>
           mk_eq.mpr
@@ -196,8 +196,8 @@ private theorem add_zero' (x : LocalizedModule S M) : x + 0 = x :=
         exact ⟨1, by rw [one_smul, mul_smul, one_smul]⟩)
     x
 
-instance hasNatSmul : SMul ℕ (LocalizedModule S M) where smul n := nsmulRec n
-#align localized_module.has_nat_smul LocalizedModule.hasNatSmul
+instance hasNatSMul : SMul ℕ (LocalizedModule S M) where smul n := nsmulRec n
+#align localized_module.has_nat_smul LocalizedModule.hasNatSMul
 
 private theorem nsmul_zero' (x : LocalizedModule S M) : (0 : ℕ) • x = 0 :=
   LocalizedModule.induction_on (fun _ _ => rfl) x
@@ -294,8 +294,8 @@ instance {A : Type*} [CommSemiring A] [Algebra R A] {S : Submonoid R} :
 
 instance {A : Type} [Ring A] [Algebra R A] {S : Submonoid R} :
     Ring (LocalizedModule S A) :=
-    { inferInstanceAs (AddCommGroup (LocalizedModule S A)),
-      inferInstanceAs (Semiring (LocalizedModule S A)) with }
+  { inferInstanceAs (AddCommGroup (LocalizedModule S A)),
+    inferInstanceAs (Semiring (LocalizedModule S A)) with }
 
 instance {A : Type _} [CommRing A] [Algebra R A] {S : Submonoid R} :
     CommRing (LocalizedModule S A) :=
@@ -309,8 +309,8 @@ theorem mk_mul_mk {A : Type*} [Semiring A] [Algebra R A] {a₁ a₂ : A} {s₁ s
   rfl
 #align localized_module.mk_mul_mk LocalizedModule.mk_mul_mk
 
-instance : SMul (Localization S) (LocalizedModule S M)
-    where smul f x :=
+instance : SMul (Localization S) (LocalizedModule S M) where
+  smul f x :=
     (Localization.liftOn f
       (fun r s =>
         (liftOn x (fun p => (mk (r • p.1) (s * p.2)))
@@ -450,8 +450,7 @@ instance : IsScalarTower R (Localization S) (LocalizedModule S M) :=
 
 instance algebra' {A : Type*} [Semiring A] [Algebra R A] : Algebra R (LocalizedModule S A) :=
   { (algebraMap (Localization S) (LocalizedModule S A)).comp (algebraMap R <| Localization S),
-    show Module R (LocalizedModule S A) by
-      infer_instance with
+    show Module R (LocalizedModule S A) by infer_instance with
     commutes' := by
       intro r x
       obtain ⟨⟨a, s⟩, rfl : mk a s = x⟩ := Quotient.exists_rep x
@@ -577,13 +576,12 @@ noncomputable def lift' (g : M →ₗ[R] M'')
   fun m =>
   m.liftOn (fun p => (h p.2).unit⁻¹.val <| g p.1) fun ⟨m, s⟩ ⟨m', s'⟩ ⟨c, eq1⟩ => by
     -- Porting note: We remove `generalize_proofs h1 h2`. This does nothing here.
-    erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← map_smul]
-    symm
-    erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff]
-    dsimp
+    dsimp only
+    simp only [Submonoid.smul_def] at eq1
+    rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← map_smul, eq_comm,
+      Module.End_algebraMap_isUnit_inv_apply_eq_iff]
     have : c • s • g m' = c • s' • g m := by
-      erw [← g.map_smul, ← g.map_smul, ← g.map_smul, ← g.map_smul, eq1]
-      rfl
+      simp only [Submonoid.smul_def, ← g.map_smul, eq1]
     have : Function.Injective (h c).unit.inv := by
       rw [Function.injective_iff_hasLeftInverse]
       refine' ⟨(h c).unit, _⟩
@@ -594,9 +592,8 @@ noncomputable def lift' (g : M →ₗ[R] M'')
     erw [Units.inv_eq_val_inv, Module.End_algebraMap_isUnit_inv_apply_eq_iff, ←
       (h c).unit⁻¹.val.map_smul]
     symm
-    erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← g.map_smul, ← g.map_smul, ← g.map_smul, ←
+    rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← g.map_smul, ← g.map_smul, ← g.map_smul, ←
       g.map_smul, eq1]
-    rfl
 #align localized_module.lift' LocalizedModule.lift'
 
 theorem lift'_mk (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
@@ -659,7 +656,7 @@ theorem lift_mk
 
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible, then
-there is a linear map `lift g ∘ mk_linear_map = g`.
+there is a linear map `lift g ∘ mkLinearMap = g`.
 -/
 theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x)) :
     (lift S g h).comp (mkLinearMap S M) = g := by
@@ -669,7 +666,7 @@ theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (M
 
 /--
 If `g` is a linear map `M → M''` such that all scalar multiplication by `s : S` is invertible and
-`l` is another linear map `LocalizedModule S M ⟶ M''` such that `l ∘ mk_linear_map = g` then
+`l` is another linear map `LocalizedModule S M ⟶ M''` such that `l ∘ mkLinearMap = g` then
 `l = lift g`
 -/
 theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
@@ -677,10 +674,10 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
     LocalizedModule.lift S g h = l := by
   ext x; induction' x using LocalizedModule.induction_on with m s
   rw [LocalizedModule.lift_mk]
-  erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← hl, LinearMap.coe_comp,
+  rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← hl, LinearMap.coe_comp,
     Function.comp_apply, LocalizedModule.mkLinearMap_apply, ← l.map_smul, LocalizedModule.smul'_mk]
   congr 1; rw [LocalizedModule.mk_eq]
-  refine' ⟨1, _⟩; simp only [one_smul]; rfl
+  refine' ⟨1, _⟩; simp only [one_smul, Submonoid.smul_def]
 #align localized_module.lift_unique LocalizedModule.lift_unique
 
 end LocalizedModule
@@ -743,7 +740,7 @@ theorem fromLocalizedModule'_add (x y : LocalizedModule S M) :
       erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, smul_add, ←map_smul, ←map_smul,
         ←map_smul, map_add]
       congr 1
-      all_goals erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff']
+      all_goals rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff']
       · erw [mul_smul, f.map_smul]
         rfl
       · erw [mul_comm, f.map_smul, mul_smul]
@@ -782,18 +779,18 @@ theorem fromLocalizedModule.inj : Function.Injective <| fromLocalizedModule S f
   induction' y using LocalizedModule.induction_on with a' b'
   simp only [fromLocalizedModule_mk] at eq1
   -- Porting note: We remove `generalize_proofs h1 h2`.
-  erw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← LinearMap.map_smul,
+  rw [Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← LinearMap.map_smul,
     Module.End_algebraMap_isUnit_inv_apply_eq_iff'] at eq1
   erw [LocalizedModule.mk_eq, ← IsLocalizedModule.eq_iff_exists S f,
     f.map_smul, f.map_smul, eq1]
-  rfl
+  rw [Submonoid.coe_subtype]
 #align is_localized_module.from_localized_module.inj IsLocalizedModule.fromLocalizedModule.inj
 
 theorem fromLocalizedModule.surj : Function.Surjective <| fromLocalizedModule S f := fun x =>
   let ⟨⟨m, s⟩, eq1⟩ := IsLocalizedModule.surj S f x
   ⟨LocalizedModule.mk m s, by
-    rw [fromLocalizedModule_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← eq1]
-    rfl⟩
+    rw [fromLocalizedModule_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, ← eq1,
+      Submonoid.smul_def]⟩
 #align is_localized_module.from_localized_module.surj IsLocalizedModule.fromLocalizedModule.surj
 
 theorem fromLocalizedModule.bij : Function.Bijective <| fromLocalizedModule S f :=
@@ -853,9 +850,7 @@ noncomputable def lift (g : M →ₗ[R] M'')
 theorem lift_comp (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x)) :
     (lift S f g h).comp f = g := by
   dsimp only [IsLocalizedModule.lift]
-  rw [LinearMap.comp_assoc]
-  convert LocalizedModule.lift_comp S g h
-  exact iso_symm_comp _ _
+  rw [LinearMap.comp_assoc, iso_symm_comp, LocalizedModule.lift_comp S g h]
 #align is_localized_module.lift_comp IsLocalizedModule.lift_comp
 
 theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R (Module.End R M'')) x))
@@ -868,7 +863,9 @@ theorem lift_unique (g : M →ₗ[R] M'') (h : ∀ x : S, IsUnit ((algebraMap R
   · rw [LinearMap.comp_assoc, ← hl]
     congr 1
     ext x
-    erw [fromLocalizedModule_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, one_smul]
+    rw [LinearMap.comp_apply, LocalizedModule.mkLinearMap_apply, LinearEquiv.coe_coe, iso_apply,
+      fromLocalizedModule'_mk, Module.End_algebraMap_isUnit_inv_apply_eq_iff, OneMemClass.coe_one,
+      one_smul]
 #align is_localized_module.lift_unique IsLocalizedModule.lift_unique
 
 /-- Universal property from localized module:
@@ -948,8 +945,8 @@ variable {S}
 @[simp]
 theorem mk'_cancel (m : M) (s : S) : mk' f (s • m) s = f m := by
   delta mk'
-  rw [LocalizedModule.mk_cancel, ← mk'_one S f]
-  rfl
+  rw [LocalizedModule.mk_cancel, ← mk'_one S f, fromLocalizedModule_mk,
+    Module.End_algebraMap_isUnit_inv_apply_eq_iff, OneMemClass.coe_one, mk'_one, one_smul]
 #align is_localized_module.mk'_cancel IsLocalizedModule.mk'_cancel
 
 @[simp]

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -268,10 +268,10 @@ instance {A : Type _} [Semiring A] [Algebra R A] {S : Submonoid R} :
         mul_right_comm]
     zero_mul := by
       rintro ⟨a, s⟩
-      exact mk_eq.mpr ⟨1, by simp only [MulZeroClass.zero_mul, smul_zero]⟩
+      exact mk_eq.mpr ⟨1, by simp only [zero_mul, smul_zero]⟩
     mul_zero := by
       rintro ⟨a, s⟩
-      exact mk_eq.mpr ⟨1, by simp only [MulZeroClass.mul_zero, smul_zero]⟩
+      exact mk_eq.mpr ⟨1, by simp only [mul_zero, smul_zero]⟩
     mul_assoc := by
       rintro ⟨a₁, s₁⟩ ⟨a₂, s₂⟩ ⟨a₃, s₃⟩
       apply mk_eq.mpr _

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

This has nice performance benefits.

@@ -116,24 +116,24 @@ theorem induction_on₂ {β : LocalizedModule S M → LocalizedModule S M → Pr
 /-- If `f : M × S → α` respects the equivalence relation `LocalizedModule.r`, then
 `f` descents to a map `LocalizedModule M S → α`.
 -/
-def liftOn {α : Type _} (x : LocalizedModule S M) (f : M × S → α)
+def liftOn {α : Type*} (x : LocalizedModule S M) (f : M × S → α)
     (wd : ∀ (p p' : M × S), p ≈ p' → f p = f p') : α :=
   Quotient.liftOn x f wd
 #align localized_module.lift_on LocalizedModule.liftOn
 
-theorem liftOn_mk {α : Type _} {f : M × S → α} (wd : ∀ (p p' : M × S), p ≈ p' → f p = f p')
+theorem liftOn_mk {α : Type*} {f : M × S → α} (wd : ∀ (p p' : M × S), p ≈ p' → f p = f p')
     (m : M) (s : S) : liftOn (mk m s) f wd = f ⟨m, s⟩ := by convert Quotient.liftOn_mk f wd ⟨m, s⟩
 #align localized_module.lift_on_mk LocalizedModule.liftOn_mk
 
 /-- If `f : M × S → M × S → α` respects the equivalence relation `LocalizedModule.r`, then
 `f` descents to a map `LocalizedModule M S → LocalizedModule M S → α`.
 -/
-def liftOn₂ {α : Type _} (x y : LocalizedModule S M) (f : M × S → M × S → α)
+def liftOn₂ {α : Type*} (x y : LocalizedModule S M) (f : M × S → M × S → α)
     (wd : ∀ (p q p' q' : M × S), p ≈ p' → q ≈ q' → f p q = f p' q') : α :=
   Quotient.liftOn₂ x y f wd
 #align localized_module.lift_on₂ LocalizedModule.liftOn₂
 
-theorem liftOn₂_mk {α : Type _} (f : M × S → M × S → α)
+theorem liftOn₂_mk {α : Type*} (f : M × S → M × S → α)
     (wd : ∀ (p q p' q' : M × S), p ≈ p' → q ≈ q' → f p q = f p' q') (m m' : M)
     (s s' : S) : liftOn₂ (mk m s) (mk m' s') f wd = f ⟨m, s⟩ ⟨m', s'⟩ := by
   convert Quotient.liftOn₂_mk f wd _ _
@@ -216,7 +216,7 @@ instance : AddCommMonoid (LocalizedModule S M) where
   nsmul_succ := nsmul_succ'
   add_comm := add_comm'
 
-instance {M : Type _} [AddCommGroup M] [Module R M] : AddCommGroup (LocalizedModule S M) :=
+instance {M : Type*} [AddCommGroup M] [Module R M] : AddCommGroup (LocalizedModule S M) :=
   { show AddCommMonoid (LocalizedModule S M) by infer_instance with
     neg := fun p =>
       liftOn p (fun x => LocalizedModule.mk (-x.1) x.2) fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => by
@@ -233,7 +233,7 @@ instance {M : Type _} [AddCommGroup M] [Module R M] : AddCommGroup (LocalizedMod
       rw [liftOn_mk, mk_add_mk]
       simp }
 
-theorem mk_neg {M : Type _} [AddCommGroup M] [Module R M] {m : M} {s : S} : mk (-m) s = -mk m s :=
+theorem mk_neg {M : Type*} [AddCommGroup M] [Module R M] {m : M} {s : S} : mk (-m) s = -mk m s :=
   rfl
 #align localized_module.mk_neg LocalizedModule.mk_neg
 
@@ -285,7 +285,7 @@ instance {A : Type _} [Semiring A] [Algebra R A] {S : Submonoid R} :
       rintro ⟨a, s⟩
       exact mk_eq.mpr ⟨1, by simp only [mul_one, one_smul]⟩ }
 
-instance {A : Type _} [CommSemiring A] [Algebra R A] {S : Submonoid R} :
+instance {A : Type*} [CommSemiring A] [Algebra R A] {S : Submonoid R} :
     CommSemiring (LocalizedModule S A) :=
   { show Semiring (LocalizedModule S A) by infer_instance with
     mul_comm := by
@@ -304,7 +304,7 @@ instance {A : Type _} [CommRing A] [Algebra R A] {S : Submonoid R} :
       rintro ⟨a₁, s₁⟩ ⟨a₂, s₂⟩
       exact mk_eq.mpr ⟨1, by simp only [one_smul, mul_comm]⟩ }
 
-theorem mk_mul_mk {A : Type _} [Semiring A] [Algebra R A] {a₁ a₂ : A} {s₁ s₂ : S} :
+theorem mk_mul_mk {A : Type*} [Semiring A] [Algebra R A] {a₁ a₂ : A} {s₁ s₂ : S} :
     mk a₁ s₁ * mk a₂ s₂ = mk (a₁ * a₂) (s₁ * s₂) :=
   rfl
 #align localized_module.mk_mul_mk LocalizedModule.mk_mul_mk
@@ -420,7 +420,7 @@ theorem smul'_mk (r : R) (s : S) (m : M) : r • mk m s = mk (r • m) s := by
   erw [mk_smul_mk r m 1 s, one_mul]
 #align localized_module.smul'_mk LocalizedModule.smul'_mk
 
-instance {A : Type _} [Semiring A] [Algebra R A] :
+instance {A : Type*} [Semiring A] [Algebra R A] :
     Algebra (Localization S) (LocalizedModule S A) :=
   Algebra.ofModule
     (by
@@ -438,7 +438,7 @@ instance {A : Type _} [Semiring A] [Algebra R A] :
       rw [mk_mul_mk, ← Localization.mk_eq_mk', mk_smul_mk, mk_smul_mk, mk_mul_mk, mul_left_comm,
         mul_smul_comm])
 
-theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
+theorem algebraMap_mk {A : Type*} [Semiring A] [Algebra R A] (a : R) (s : S) :
     algebraMap _ _ (Localization.mk a s) = mk (algebraMap R A a) s := by
   rw [Algebra.algebraMap_eq_smul_one]
   change _ • mk _ _ = _
@@ -448,7 +448,7 @@ theorem algebraMap_mk {A : Type _} [Semiring A] [Algebra R A] (a : R) (s : S) :
 instance : IsScalarTower R (Localization S) (LocalizedModule S M) :=
   RestrictScalars.isScalarTower R (Localization S) (LocalizedModule S M)
 
-instance algebra' {A : Type _} [Semiring A] [Algebra R A] : Algebra R (LocalizedModule S A) :=
+instance algebra' {A : Type*} [Semiring A] [Algebra R A] : Algebra R (LocalizedModule S A) :=
   { (algebraMap (Localization S) (LocalizedModule S A)).comp (algebraMap R <| Localization S),
     show Module R (LocalizedModule S A) by
       infer_instance with
@@ -538,9 +538,9 @@ section IsLocalizedModule
 
 universe u v
 
-variable {R : Type _} [CommRing R] (S : Submonoid R)
+variable {R : Type*} [CommRing R] (S : Submonoid R)
 
-variable {M M' M'' : Type _} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid M'']
+variable {M M' M'' : Type*} [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid M'']
 
 variable [Module R M] [Module R M'] [Module R M''] (f : M →ₗ[R] M') (g : M →ₗ[R] M'')
 
@@ -980,25 +980,25 @@ theorem mk'_eq_mk'_iff (m₁ m₂ : M) (s₁ s₂ : S) :
   simp_rw [eq_comm]
 #align is_localized_module.mk'_eq_mk'_iff IsLocalizedModule.mk'_eq_mk'_iff
 
-theorem mk'_neg {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
+theorem mk'_neg {M M' : Type*} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m : M) (s : S) : mk' f (-m) s = -mk' f m s := by
   delta mk'
   rw [LocalizedModule.mk_neg, map_neg]
 #align is_localized_module.mk'_neg IsLocalizedModule.mk'_neg
 
-theorem mk'_sub {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
+theorem mk'_sub {M M' : Type*} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m₁ m₂ : M) (s : S) :
     mk' f (m₁ - m₂) s = mk' f m₁ s - mk' f m₂ s := by
   rw [sub_eq_add_neg, sub_eq_add_neg, mk'_add, mk'_neg]
 #align is_localized_module.mk'_sub IsLocalizedModule.mk'_sub
 
-theorem mk'_sub_mk' {M M' : Type _} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
+theorem mk'_sub_mk' {M M' : Type*} [AddCommGroup M] [AddCommGroup M'] [Module R M] [Module R M']
     (f : M →ₗ[R] M') [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ - mk' f m₂ s₂ = mk' f (s₂ • m₁ - s₁ • m₂) (s₁ * s₂) := by
   rw [sub_eq_add_neg, ← mk'_neg, mk'_add_mk', smul_neg, ← sub_eq_add_neg]
 #align is_localized_module.mk'_sub_mk' IsLocalizedModule.mk'_sub_mk'
 
-theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Module R M]
+theorem mk'_mul_mk'_of_map_mul {M M' : Type*} [Semiring M] [Semiring M'] [Module R M]
     [Algebra R M'] (f : M →ₗ[R] M') (hf : ∀ m₁ m₂, f (m₁ * m₂) = f m₁ * f m₂)
     [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ * mk' f m₂ s₂ = mk' f (m₁ * m₂) (s₁ * s₂) := by
@@ -1009,7 +1009,7 @@ theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Modul
   simp_rw [← Submonoid.smul_def, mk'_cancel, smul_eq_mul, hf]
 #align is_localized_module.mk'_mul_mk'_of_map_mul IsLocalizedModule.mk'_mul_mk'_of_map_mul
 
-theorem mk'_mul_mk' {M M' : Type _} [Semiring M] [Semiring M'] [Algebra R M] [Algebra R M']
+theorem mk'_mul_mk' {M M' : Type*} [Semiring M] [Semiring M'] [Algebra R M] [Algebra R M']
     (f : M →ₐ[R] M') [IsLocalizedModule S f.toLinearMap] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f.toLinearMap m₁ s₁ * mk' f.toLinearMap m₂ s₂ = mk' f.toLinearMap (m₁ * m₂) (s₁ * s₂) :=
   mk'_mul_mk'_of_map_mul f.toLinearMap f.map_mul m₁ m₂ s₁ s₂
@@ -1053,7 +1053,7 @@ theorem mk'_surjective : Function.Surjective (Function.uncurry <| mk' f : M × S
 
 section Algebra
 
-theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [Algebra R S]
+theorem mkOfAlgebra {R S S' : Type*} [CommRing R] [CommRing S] [CommRing S'] [Algebra R S]
     [Algebra R S'] (M : Submonoid R) (f : S →ₐ[R] S') (h₁ : ∀ x ∈ M, IsUnit (algebraMap R S' x))
     (h₂ : ∀ y, ∃ x : S × M, x.2 • y = f x.1) (h₃ : ∀ x, f x = 0 → ∃ m : M, m • x = 0) :
     IsLocalizedModule M f.toLinearMap := by
@@ -1082,7 +1082,7 @@ theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [A
 
 end Algebra
 
-variable {A : Type _}
+variable {A : Type*}
   [CommRing A] [Algebra R A] [Module A M'] [IsScalarTower R A M'] [IsLocalization S A]
 
 

Note that the module instance was already generalized; we were just missing the fact that when combined with the existing ring instance, the result was an algebra.

This also moves some lemmas about IsUnit (_ : Module.End R M) to an earlier file as they are nothing to do with Algebra.

@@ -1003,7 +1003,7 @@ theorem mk'_mul_mk'_of_map_mul {M M' : Type _} [Semiring M] [Semiring M'] [Modul
     [IsLocalizedModule S f] (m₁ m₂ : M) (s₁ s₂ : S) :
     mk' f m₁ s₁ * mk' f m₂ s₂ = mk' f (m₁ * m₂) (s₁ * s₂) := by
   symm
-  apply (Module.End_algebraMap_isUnit_inv_apply_eq_iff _ _ _).mpr
+  apply (Module.End_algebraMap_isUnit_inv_apply_eq_iff _ _ _ _).mpr
   simp_rw [Submonoid.coe_mul, ← smul_eq_mul]
   rw [smul_smul_smul_comm, ← mk'_smul, ← mk'_smul]
   simp_rw [← Submonoid.smul_def, mk'_cancel, smul_eq_mul, hf]

Port of leanprover-community/mathlib#17973

Follow up work:

• add IsPushout when M is a CommRing.

Co-authored-by: Calvin Lee <calvins.lee@utah.edu> Co-authored-by: Calvin Lee <pounce@integraldoma.in>

@@ -5,7 +5,9 @@ Authors: Andrew Yang, Jujian Zhang
 -/
 import Mathlib.GroupTheory.MonoidLocalization
 import Mathlib.RingTheory.Localization.Basic
+import Mathlib.RingTheory.Localization.Module
 import Mathlib.Algebra.Algebra.RestrictScalars
+import Mathlib.RingTheory.IsTensorProduct
 
 #align_import algebra.module.localized_module from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
 
@@ -31,6 +33,7 @@ localize `M` by `S`. This gives us a `Localization S`-module.
   we have `mk r s • mk m t = mk (r • m) (s * t)` where `mk r s : Localization S` is localized ring
   by `S`.
 * `LocalizedModule.isModule` : `LocalizedModule M S` is a `Localization S`-module.
+* `IsLocalizedModule.IsBaseChange` : A localization of modules is a base change.
 
 ## Future work
 
@@ -1079,6 +1082,32 @@ theorem mkOfAlgebra {R S S' : Type _} [CommRing R] [CommRing S] [CommRing S'] [A
 
 end Algebra
 
+variable {A : Type _}
+  [CommRing A] [Algebra R A] [Module A M'] [IsScalarTower R A M'] [IsLocalization S A]
+
+
+/-- If `(f : M →ₗ[R] M')` is a localization of modules, then the map
+`(localization S) × M → N, (s, m) ↦ s • f m` is the tensor product (insomuch as it is the universal
+bilinear map).
+In particular, there is an isomorphism between `LocalizedModule S M` and `(Localization S) ⊗[R] M`
+given by `m/s ↦ (1/s) ⊗ₜ m`.
+-/
+theorem isBaseChange : IsBaseChange A f := by
+  refine' IsBaseChange.of_lift_unique _ (fun Q _ _ _ _ g ↦ _)
+  have := IsLocalizedModule.is_universal S f g <| by
+    intro s
+    simp_rw [Module.End_isUnit_iff, Function.bijective_iff_existsUnique,
+      Module.algebraMap_end_apply]
+    intro q
+    refine' ⟨(IsLocalization.mk' _ 1 s : A) • q, _, _⟩
+    · simp only [← smul_assoc, IsLocalization.smul_mk'_self, map_one, one_smul]
+    · rintro q rfl
+      simp only [smul_comm _ (s : R), ← smul_assoc, IsLocalization.smul_mk'_self, map_one, one_smul]
+  rcases this with ⟨ℓ, rfl, h₂⟩
+  refine' ⟨ℓ.extendScalarsOfIsLocalization S A, by simp, fun g'' h ↦ _⟩
+  ext x
+  simp [← h₂ (LinearMap.restrictScalars R g'') h]
+
 end IsLocalizedModule
 
 end IsLocalizedModule

@@ -18,7 +18,7 @@ localize `M` by `S`. This gives us a `Localization S`-module.
 ## Main definitions
 
 * `LocalizedModule.r` : the equivalence relation defining this localization, namely
-  `(m, s) ≈ (m', s')` if and only if if there is some `u : S` such that `u • s' • m = u • s • m'`.
+  `(m, s) ≈ (m', s')` if and only if there is some `u : S` such that `u • s' • m = u • s • m'`.
 * `LocalizedModule M S` : the localized module by `S`.
 * `LocalizedModule.mk`  : the canonical map sending `(m, s) : M × S ↦ m/s : LocalizedModule M S`
 * `LocalizedModule.liftOn` : any well defined function `f : M × S → α` respecting `r` descents to

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang, Jujian Zhang
-
-! This file was ported from Lean 3 source module algebra.module.localized_module
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.MonoidLocalization
 import Mathlib.RingTheory.Localization.Basic
 import Mathlib.Algebra.Algebra.RestrictScalars
 
+#align_import algebra.module.localized_module from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
+
 /-!
 # Localized Module
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -503,7 +503,7 @@ def divBy (s : S) : LocalizedModule S M →ₗ[R] LocalizedModule S M where
     x.inductionOn <| by
       intro
       dsimp only
-      change liftOn (mk _ _) _ _  = r • (liftOn (mk _ _) _ _)
+      change liftOn (mk _ _) _ _ = r • (liftOn (mk _ _) _ _)
       simp [LocalizedModule.liftOn_mk, smul'_mk]
 #align localized_module.div_by LocalizedModule.divBy
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -63,7 +63,7 @@ theorem r.isEquiv : IsEquiv _ (r S M) :=
       -- Put everything in the same shape, sorting the terms using `simp`
       have hu1' := congr_arg ((· • ·) (u2 * s3)) hu1.symm
       have hu2' := congr_arg ((· • ·) (u1 * s1)) hu2.symm
-      simp only [← mul_smul, smul_assoc, mul_assoc, mul_comm, mul_left_comm] at hu1' hu2'⊢
+      simp only [← mul_smul, smul_assoc, mul_assoc, mul_comm, mul_left_comm] at hu1' hu2' ⊢
       rw [hu2', hu1']
     symm := fun ⟨m1, s1⟩ ⟨m2, s2⟩ ⟨u, hu⟩ => ⟨u, hu.symm⟩ }
 #align localized_module.r.is_equiv LocalizedModule.r.isEquiv
@@ -247,7 +247,7 @@ instance {A : Type _} [Semiring A] [Algebra R A] {S : Submonoid R} :
           rintro ⟨a₁, s₁⟩ ⟨a₂, s₂⟩ ⟨b₁, t₁⟩ ⟨b₂, t₂⟩ ⟨u₁, e₁⟩ ⟨u₂, e₂⟩
           rw [mk_eq]
           use u₁ * u₂
-          dsimp only at e₁ e₂⊢
+          dsimp only at e₁ e₂ ⊢
           rw [eq_comm]
           trans (u₁ • t₁ • a₁) • u₂ • t₂ • a₂
           rw [e₁, e₂]; swap; rw [eq_comm]
@@ -319,7 +319,7 @@ instance : SMul (Localization S) (LocalizedModule S M)
             refine' mk_eq.mpr ⟨u, _⟩
             have h' := congr_arg ((· • ·) (s • r)) h
             simp only [← mul_smul, smul_eq_mul, mul_comm, mul_left_comm, Submonoid.smul_def,
-              Submonoid.coe_mul] at h'⊢
+              Submonoid.coe_mul] at h' ⊢
             rw [h'])))
       (by
         induction' x using LocalizedModule.induction_on with m t
@@ -328,8 +328,8 @@ instance : SMul (Localization S) (LocalizedModule S M)
         obtain ⟨u, eq1⟩ := Localization.r_iff_exists.mp h
         use u
         have eq1' := congr_arg (· • t • m) eq1
-        simp only [← mul_smul, smul_assoc, Submonoid.smul_def, Submonoid.coe_mul] at eq1'⊢
-        ring_nf  at eq1'⊢
+        simp only [← mul_smul, smul_assoc, Submonoid.smul_def, Submonoid.coe_mul] at eq1' ⊢
+        ring_nf at eq1' ⊢
         rw [eq1']))
 
 theorem mk_smul_mk (r : R) (m : M) (s t : S) :

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -559,7 +559,7 @@ attribute [nolint docBlame] IsLocalizedModule.map_units IsLocalizedModule.surj'
 
 -- Porting note: Manually added to make `S` and `f` explicit.
 lemma IsLocalizedModule.surj [IsLocalizedModule S f] (y : M') : ∃ x : M × S, x.2 • y = f x.1 :=
-surj' y
+  surj' y
 
 -- Porting note: Manually added to make `S` and `f` explicit.
 lemma IsLocalizedModule.eq_iff_exists [IsLocalizedModule S f] {x₁ x₂} :

• depends on: #3414

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: yuma-mizuno <mizuno.y.aj@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Mauricio Collares <mauricio@collares.org> Co-authored-by: Gabriel Ebner <gebner@gebner.org>