ring_theory.localization.basic ⟷ Mathlib.RingTheory.Localization.Basic

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

@@ -1239,10 +1239,10 @@ theorem mk_algebraMap {A : Type _} [CommSemiring A] [Algebra A R] (m : A) :
 #align localization.mk_algebra_map Localization.mk_algebraMap
 -/
 
-#print Localization.mk_nat_cast /-
-theorem mk_nat_cast (m : ℕ) : (mk m 1 : Localization M) = m := by
+#print Localization.mk_natCast /-
+theorem mk_natCast (m : ℕ) : (mk m 1 : Localization M) = m := by
   simpa using @mk_algebra_map R _ M ℕ _ _ m
-#align localization.mk_nat_cast Localization.mk_nat_cast
+#align localization.mk_nat_cast Localization.mk_natCast
 -/
 
 variable [IsLocalization M S]
@@ -1363,10 +1363,10 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b
 #align localization.sub_mk Localization.sub_mk
 -/
 
-#print Localization.mk_int_cast /-
-theorem mk_int_cast (m : ℤ) : (mk m 1 : Localization M) = m := by
+#print Localization.mk_intCast /-
+theorem mk_intCast (m : ℤ) : (mk m 1 : Localization M) = m := by
   simpa using @mk_algebra_map R _ M ℤ _ _ m
-#align localization.mk_int_cast Localization.mk_int_cast
+#align localization.mk_int_cast Localization.mk_intCast
 -/
 
 end Localization

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

@@ -7,7 +7,7 @@ import Algebra.Algebra.Tower
 import Algebra.Ring.Equiv
 import GroupTheory.MonoidLocalization
 import RingTheory.Ideal.Basic
-import RingTheory.NonZeroDivisors
+import Algebra.GroupWithZero.NonZeroDivisors
 import Tactic.RingExp
 
 #align_import ring_theory.localization.basic from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
@@ -1079,7 +1079,7 @@ instance : CommSemiring (Localization M) :=
     nsmul_zero := fun x =>
       Localization.induction_on x fun x => by simp only [smul_mk, zero_nsmul, mk_zero]
     nsmul_succ := fun n x =>
-      Localization.induction_on x fun x => by simp only [smul_mk, succ_nsmul, add_mk_self]
+      Localization.induction_on x fun x => by simp only [smul_mk, succ_nsmul', add_mk_self]
     add_assoc := fun m n k =>
       Localization.induction_on₃ m n k
         (by

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

@@ -229,7 +229,7 @@ theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R
 #print IsLocalization.eq_zero_of_fst_eq_zero /-
 theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebraMap R S x)
     (hx : x = 0) : z = 0 := by
-  rw [hx, (algebraMap R S).map_zero] at h 
+  rw [hx, (algebraMap R S).map_zero] at h
   exact (IsUnit.mul_left_eq_zero (IsLocalization.map_units S y)).1 h
 #align is_localization.eq_zero_of_fst_eq_zero IsLocalization.eq_zero_of_fst_eq_zero
 -/
@@ -380,10 +380,10 @@ theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R
   constructor <;> intro h
   · rw [← mk'_spec S x y, mul_comm]
     exact I.mul_mem_left ((algebraMap R S) y) h
-  · rw [← mk'_spec S x y] at h 
+  · rw [← mk'_spec S x y] at h
     obtain ⟨b, hb⟩ := isUnit_iff_exists_inv.1 (map_units S y)
     have := I.mul_mem_left b h
-    rwa [mul_comm, mul_assoc, hb, mul_one] at this 
+    rwa [mul_comm, mul_assoc, hb, mul_one] at this
 #align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iff
 -/
 
@@ -900,8 +900,8 @@ theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃
     exact (h.commutes y).symm
   · intro y
     obtain ⟨⟨x, s⟩, e⟩ := IsLocalization.surj M (h.symm y)
-    apply_fun h at e 
-    simp only [h.map_mul, h.apply_symm_apply, h.commutes] at e 
+    apply_fun h at e
+    simp only [h.map_mul, h.apply_symm_apply, h.commutes] at e
     exact ⟨⟨x, s⟩, e⟩
   · intro x y
     rw [← h.symm.to_equiv.injective.eq_iff, ← IsLocalization.eq_iff_exists M S, ← h.symm.commutes, ←
@@ -984,9 +984,9 @@ theorem nonZeroDivisors_le_comap [IsLocalization M S] :
   rintro a ha b (e : b * algebraMap R S a = 0)
   obtain ⟨x, s, rfl⟩ := mk'_surjective M b
   rw [← @mk'_one R _ M, ← mk'_mul, ← (algebraMap R S).map_zero, ← @mk'_one R _ M,
-    IsLocalization.eq] at e 
+    IsLocalization.eq] at e
   obtain ⟨c, e⟩ := e
-  rw [MulZeroClass.mul_zero, MulZeroClass.mul_zero, Submonoid.coe_one, one_mul, ← mul_assoc] at e 
+  rw [MulZeroClass.mul_zero, MulZeroClass.mul_zero, Submonoid.coe_one, one_mul, ← mul_assoc] at e
   rw [mk'_eq_zero_iff]
   exact ⟨c, ha _ e⟩
 #align is_localization.non_zero_divisors_le_comap IsLocalization.nonZeroDivisors_le_comap
@@ -1381,7 +1381,7 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
   rw [← (algebraMap R S).map_zero]
   constructor <;> intro h
   · cases' (eq_iff_exists M S).mp h with c hc
-    rw [MulZeroClass.mul_zero, mul_comm] at hc 
+    rw [MulZeroClass.mul_zero, mul_comm] at hc
     exact hM c.2 x hc
   · rw [h]
 #align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iff
@@ -1392,7 +1392,7 @@ protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraM
   by
   rw [injective_iff_map_eq_zero (algebraMap R S)]
   intro a ha
-  rwa [to_map_eq_zero_iff S hM] at ha 
+  rwa [to_map_eq_zero_iff S hM] at ha
 #align is_localization.injective IsLocalization.injective
 -/
 
@@ -1419,7 +1419,7 @@ theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDiv
   by
   have hsec := sec_spec M x
   intro hfst
-  rw [hfst, map_zero, mul_eq_zero, _root_.map_eq_zero_iff] at hsec 
+  rw [hfst, map_zero, mul_eq_zero, _root_.map_eq_zero_iff] at hsec
   · exact Or.elim hsec hx (sec_snd_ne_zero hM x)
   · exact IsLocalization.injective S hM
 #align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zero
@@ -1436,11 +1436,11 @@ theorem map_injective_of_injective (hg : Function.Injective g)
   rw [injective_iff_map_eq_zero]
   intro z hz
   obtain ⟨a, b, rfl⟩ := mk'_surjective M z
-  rw [map_mk', mk'_eq_zero_iff] at hz 
+  rw [map_mk', mk'_eq_zero_iff] at hz
   obtain ⟨⟨m', hm'⟩, hm⟩ := hz
-  rw [Submonoid.mem_map] at hm' 
+  rw [Submonoid.mem_map] at hm'
   obtain ⟨n, hn, hnm⟩ := hm'
-  rw [Subtype.coe_mk, ← hnm, ← map_mul, ← map_zero g] at hm 
+  rw [Subtype.coe_mk, ← hnm, ← map_mul, ← map_zero g] at hm
   rw [mk'_eq_zero_iff]
   exact ⟨⟨n, hn⟩, hg hm⟩
 #align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injective
@@ -1465,7 +1465,7 @@ theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [Is
       have :
         z * w * algebraMap A S y.2 * algebraMap A S x.2 = algebraMap A S x.1 * algebraMap A S y.1 :=
         by rw [mul_assoc z, hy, ← hx] <;> ring
-      rw [h, MulZeroClass.zero_mul, MulZeroClass.zero_mul, ← (algebraMap A S).map_hMul] at this 
+      rw [h, MulZeroClass.zero_mul, MulZeroClass.zero_mul, ← (algebraMap A S).map_hMul] at this
       cases' eq_zero_or_eq_zero_of_mul_eq_zero ((to_map_eq_zero_iff S hM).mp this.symm) with H H
       · exact Or.inl (eq_zero_of_fst_eq_zero hx H)
       · exact Or.inr (eq_zero_of_fst_eq_zero hy H) }

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

@@ -98,9 +98,9 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 variable [Algebra R S] {P : Type _} [CommSemiring P]
 
 #print IsLocalization /-
-/- ./././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 typeclass `is_localization (M : submodule R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
 class IsLocalization : Prop where

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

@@ -1624,7 +1624,7 @@ theorem IsLocalization.algebraMap_apply_eq_map_map_submonoid (x) :
     algebraMap Rₘ Sₘ x =
       map Sₘ (algebraMap R S)
         (show _ ≤ (Algebra.algebraMapSubmonoid S M).comap _ from M.le_comap_map) x :=
-  FunLike.congr_fun (IsLocalization.algebraMap_eq_map_map_submonoid _ _ _ _) x
+  DFunLike.congr_fun (IsLocalization.algebraMap_eq_map_map_submonoid _ _ _ _) x
 #align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoid
 -/
 

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

@@ -98,9 +98,9 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 variable [Algebra R S] {P : Type _} [CommSemiring P]
 
 #print IsLocalization /-
-/- ./././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 typeclass `is_localization (M : submodule R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
 class IsLocalization : Prop where

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

@@ -3,12 +3,12 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
 -/
-import Mathbin.Algebra.Algebra.Tower
-import Mathbin.Algebra.Ring.Equiv
-import Mathbin.GroupTheory.MonoidLocalization
-import Mathbin.RingTheory.Ideal.Basic
-import Mathbin.RingTheory.NonZeroDivisors
-import Mathbin.Tactic.RingExp
+import Algebra.Algebra.Tower
+import Algebra.Ring.Equiv
+import GroupTheory.MonoidLocalization
+import RingTheory.Ideal.Basic
+import RingTheory.NonZeroDivisors
+import Tactic.RingExp
 
 #align_import ring_theory.localization.basic from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
 
@@ -98,9 +98,9 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 variable [Algebra R S] {P : Type _} [CommSemiring P]
 
 #print IsLocalization /-
-/- ./././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 typeclass `is_localization (M : submodule R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
 class IsLocalization : Prop where
@@ -1058,7 +1058,7 @@ theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b
 #align localization.add_mk_self Localization.add_mk_self
 -/
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
 private unsafe def tac :=
   sorry
 

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

@@ -1465,7 +1465,7 @@ theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [Is
       have :
         z * w * algebraMap A S y.2 * algebraMap A S x.2 = algebraMap A S x.1 * algebraMap A S y.1 :=
         by rw [mul_assoc z, hy, ← hx] <;> ring
-      rw [h, MulZeroClass.zero_mul, MulZeroClass.zero_mul, ← (algebraMap A S).map_mul] at this 
+      rw [h, MulZeroClass.zero_mul, MulZeroClass.zero_mul, ← (algebraMap A S).map_hMul] at this 
       cases' eq_zero_or_eq_zero_of_mul_eq_zero ((to_map_eq_zero_iff S hM).mp this.symm) with H H
       · exact Or.inl (eq_zero_of_fst_eq_zero hx H)
       · exact Or.inr (eq_zero_of_fst_eq_zero hy H) }

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -1062,12 +1062,12 @@ theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b
 private unsafe def tac :=
   sorry
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.703018979.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.703018979.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.703018979.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.703018979.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.703018979.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.703018979.tac -/
 instance : CommSemiring (Localization M) :=
   { Localization.commMonoidWithZero M with
     zero := 0

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

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.basic
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Tower
 import Mathbin.Algebra.Ring.Equiv
@@ -15,6 +10,8 @@ import Mathbin.RingTheory.Ideal.Basic
 import Mathbin.RingTheory.NonZeroDivisors
 import Mathbin.Tactic.RingExp
 
+#align_import ring_theory.localization.basic from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
 /-!
 # Localizations of commutative rings
 

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

@@ -101,9 +101,9 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 variable [Algebra R S] {P : Type _} [CommSemiring P]
 
 #print IsLocalization /-
-/- ./././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 typeclass `is_localization (M : submodule R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
 class IsLocalization : Prop where
@@ -125,6 +125,7 @@ section
 
 variable (M)
 
+#print IsLocalization.of_le /-
 theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (algebraMap R S r)) :
     IsLocalization N S :=
   { map_units := fun r => h₂ r r.2
@@ -138,6 +139,7 @@ theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (al
         simpa only [SetLike.coe_mk, map_mul, (h₂ c c.2).mul_right_inj] using
           congr_arg (algebraMap R S) h }
 #align is_localization.of_le IsLocalization.of_le
+-/
 
 variable (S)
 
@@ -161,64 +163,83 @@ abbrev toLocalizationMap : Submonoid.LocalizationMap M S :=
 #align is_localization.to_localization_map IsLocalization.toLocalizationMap
 -/
 
+#print IsLocalization.toLocalizationMap_toMap /-
 @[simp]
 theorem toLocalizationMap_toMap : (toLocalizationMap M S).toMap = (algebraMap R S : R →*₀ S) :=
   rfl
 #align is_localization.to_localization_map_to_map IsLocalization.toLocalizationMap_toMap
+-/
 
+#print IsLocalization.toLocalizationMap_toMap_apply /-
 theorem toLocalizationMap_toMap_apply (x) : (toLocalizationMap M S).toMap x = algebraMap R S x :=
   rfl
 #align is_localization.to_localization_map_to_map_apply IsLocalization.toLocalizationMap_toMap_apply
+-/
 
 end
 
 variable (M)
 
+#print IsLocalization.sec /-
 /-- Given a localization map `f : M →* N`, a section function sending `z : N` to some
 `(x, y) : M × S` such that `f x * (f y)⁻¹ = z`. -/
 noncomputable def sec (z : S) : R × M :=
   Classical.choose <| IsLocalization.surj _ z
 #align is_localization.sec IsLocalization.sec
+-/
 
+#print IsLocalization.toLocalizationMap_sec /-
 @[simp]
 theorem toLocalizationMap_sec : (toLocalizationMap M S).sec = sec M :=
   rfl
 #align is_localization.to_localization_map_sec IsLocalization.toLocalizationMap_sec
+-/
 
+#print IsLocalization.sec_spec /-
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x` (so this lemma is true by definition). -/
 theorem sec_spec (z : S) :
     z * algebraMap R S (IsLocalization.sec M z).2 = algebraMap R S (IsLocalization.sec M z).1 :=
   Classical.choose_spec <| IsLocalization.surj _ z
 #align is_localization.sec_spec IsLocalization.sec_spec
+-/
 
+#print IsLocalization.sec_spec' /-
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x`, so this lemma is just an application of `S`'s commutativity. -/
 theorem sec_spec' (z : S) :
     algebraMap R S (IsLocalization.sec M z).1 = algebraMap R S (IsLocalization.sec M z).2 * z := by
   rw [mul_comm, sec_spec]
 #align is_localization.sec_spec' IsLocalization.sec_spec'
+-/
 
 variable {R M}
 
+#print IsLocalization.map_right_cancel /-
 theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap R S (c * y)) :
     algebraMap R S x = algebraMap R S y :=
   (toLocalizationMap M S).map_right_cancel h
 #align is_localization.map_right_cancel IsLocalization.map_right_cancel
+-/
 
+#print IsLocalization.map_left_cancel /-
 theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R S (y * c)) :
     algebraMap R S x = algebraMap R S y :=
   (toLocalizationMap M S).map_left_cancel h
 #align is_localization.map_left_cancel IsLocalization.map_left_cancel
+-/
 
+#print IsLocalization.eq_zero_of_fst_eq_zero /-
 theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebraMap R S x)
     (hx : x = 0) : z = 0 := by
   rw [hx, (algebraMap R S).map_zero] at h 
   exact (IsUnit.mul_left_eq_zero (IsLocalization.map_units S y)).1 h
 #align is_localization.eq_zero_of_fst_eq_zero IsLocalization.eq_zero_of_fst_eq_zero
+-/
 
 variable (M S)
 
+#print IsLocalization.map_eq_zero_iff /-
 theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r = 0 :=
   by
   constructor
@@ -229,14 +250,17 @@ theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r =
     rw [← (IsLocalization.map_units S m).mul_right_inj, MulZeroClass.mul_zero, ← RingHom.map_mul,
       hm, RingHom.map_zero]
 #align is_localization.map_eq_zero_iff IsLocalization.map_eq_zero_iff
+-/
 
 variable {M}
 
+#print IsLocalization.mk' /-
 /-- `is_localization.mk' S` is the surjection sending `(x, y) : R × M` to
 `f x * (f y)⁻¹`. -/
 noncomputable def mk' (x : R) (y : M) : S :=
   (toLocalizationMap M S).mk' x y
 #align is_localization.mk' IsLocalization.mk'
+-/
 
 #print IsLocalization.mk'_sec /-
 @[simp]
@@ -245,64 +269,82 @@ theorem mk'_sec (z : S) : mk' S (IsLocalization.sec M z).1 (IsLocalization.sec M
 #align is_localization.mk'_sec IsLocalization.mk'_sec
 -/
 
+#print IsLocalization.mk'_mul /-
 theorem mk'_mul (x₁ x₂ : R) (y₁ y₂ : M) : mk' S (x₁ * x₂) (y₁ * y₂) = mk' S x₁ y₁ * mk' S x₂ y₂ :=
   (toLocalizationMap M S).mk'_mul _ _ _ _
 #align is_localization.mk'_mul IsLocalization.mk'_mul
+-/
 
+#print IsLocalization.mk'_one /-
 theorem mk'_one (x) : mk' S x (1 : M) = algebraMap R S x :=
   (toLocalizationMap M S).mk'_one _
 #align is_localization.mk'_one IsLocalization.mk'_one
+-/
 
+#print IsLocalization.mk'_spec /-
 @[simp]
 theorem mk'_spec (x) (y : M) : mk' S x y * algebraMap R S y = algebraMap R S x :=
   (toLocalizationMap M S).mk'_spec _ _
 #align is_localization.mk'_spec IsLocalization.mk'_spec
+-/
 
+#print IsLocalization.mk'_spec' /-
 @[simp]
 theorem mk'_spec' (x) (y : M) : algebraMap R S y * mk' S x y = algebraMap R S x :=
   (toLocalizationMap M S).mk'_spec' _ _
 #align is_localization.mk'_spec' IsLocalization.mk'_spec'
+-/
 
+#print IsLocalization.mk'_spec_mk /-
 @[simp]
 theorem mk'_spec_mk (x) (y : R) (hy : y ∈ M) :
     mk' S x ⟨y, hy⟩ * algebraMap R S y = algebraMap R S x :=
   mk'_spec S x ⟨y, hy⟩
 #align is_localization.mk'_spec_mk IsLocalization.mk'_spec_mk
+-/
 
+#print IsLocalization.mk'_spec'_mk /-
 @[simp]
 theorem mk'_spec'_mk (x) (y : R) (hy : y ∈ M) :
     algebraMap R S y * mk' S x ⟨y, hy⟩ = algebraMap R S x :=
   mk'_spec' S x ⟨y, hy⟩
 #align is_localization.mk'_spec'_mk IsLocalization.mk'_spec'_mk
+-/
 
 variable {S}
 
+#print IsLocalization.eq_mk'_iff_mul_eq /-
 theorem eq_mk'_iff_mul_eq {x} {y : M} {z} :
     z = mk' S x y ↔ z * algebraMap R S y = algebraMap R S x :=
   (toLocalizationMap M S).eq_mk'_iff_mul_eq
 #align is_localization.eq_mk'_iff_mul_eq IsLocalization.eq_mk'_iff_mul_eq
+-/
 
+#print IsLocalization.mk'_eq_iff_eq_mul /-
 theorem mk'_eq_iff_eq_mul {x} {y : M} {z} :
     mk' S x y = z ↔ algebraMap R S x = z * algebraMap R S y :=
   (toLocalizationMap M S).mk'_eq_iff_eq_mul
 #align is_localization.mk'_eq_iff_eq_mul IsLocalization.mk'_eq_iff_eq_mul
+-/
 
+#print IsLocalization.mk'_add_eq_iff_add_mul_eq_mul /-
 theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
     mk' S x y + z₁ = z₂ ↔ algebraMap R S x + z₁ * algebraMap R S y = z₂ * algebraMap R S y := by
   rw [← mk'_spec S x y, ← IsUnit.mul_left_inj (IsLocalization.map_units S y), right_distrib]
 #align is_localization.mk'_add_eq_iff_add_mul_eq_mul IsLocalization.mk'_add_eq_iff_add_mul_eq_mul
+-/
 
 variable (M)
 
+#print IsLocalization.mk'_surjective /-
 theorem mk'_surjective (z : S) : ∃ (x : _) (y : M), mk' S x y = z :=
   let ⟨r, hr⟩ := IsLocalization.surj _ z
   ⟨r.1, r.2, (eq_mk'_iff_mul_eq.2 hr).symm⟩
 #align is_localization.mk'_surjective IsLocalization.mk'_surjective
+-/
 
 variable (S)
 
-include M
-
 #print IsLocalization.fintype' /-
 /-- The localization of a `fintype` is a `fintype`. Cannot be an instance. -/
 noncomputable def fintype' [Fintype R] : Fintype S :=
@@ -312,25 +354,30 @@ noncomputable def fintype' [Fintype R] : Fintype S :=
 #align is_localization.fintype' IsLocalization.fintype'
 -/
 
-omit M
-
 variable {M S}
 
+#print IsLocalization.uniqueOfZeroMem /-
 /-- Localizing at a submonoid with 0 inside it leads to the trivial ring. -/
 def uniqueOfZeroMem (h : (0 : R) ∈ M) : Unique S :=
   uniqueOfZeroEqOne <| by simpa using IsLocalization.map_units S ⟨0, h⟩
 #align is_localization.unique_of_zero_mem IsLocalization.uniqueOfZeroMem
+-/
 
+#print IsLocalization.mk'_eq_iff_eq /-
 theorem mk'_eq_iff_eq {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (y₂ * x₁) = algebraMap R S (y₁ * x₂) :=
   (toLocalizationMap M S).mk'_eq_iff_eq
 #align is_localization.mk'_eq_iff_eq IsLocalization.mk'_eq_iff_eq
+-/
 
+#print IsLocalization.mk'_eq_iff_eq' /-
 theorem mk'_eq_iff_eq' {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (x₁ * y₂) = algebraMap R S (x₂ * y₁) :=
   (toLocalizationMap M S).mk'_eq_iff_eq'
 #align is_localization.mk'_eq_iff_eq' IsLocalization.mk'_eq_iff_eq'
+-/
 
+#print IsLocalization.mk'_mem_iff /-
 theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R S x ∈ I :=
   by
   constructor <;> intro h
@@ -341,113 +388,153 @@ theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R
     have := I.mul_mem_left b h
     rwa [mul_comm, mul_assoc, hb, mul_one] at this 
 #align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iff
+-/
 
+#print IsLocalization.eq /-
 protected theorem eq {a₁ b₁} {a₂ b₂ : M} :
     mk' S a₁ a₂ = mk' S b₁ b₂ ↔ ∃ c : M, ↑c * (↑b₂ * a₁) = c * (a₂ * b₁) :=
   (toLocalizationMap M S).Eq
 #align is_localization.eq IsLocalization.eq
+-/
 
+#print IsLocalization.mk'_eq_zero_iff /-
 theorem mk'_eq_zero_iff (x : R) (s : M) : mk' S x s = 0 ↔ ∃ m : M, ↑m * x = 0 := by
   rw [← (map_units S s).mul_left_inj, mk'_spec, MulZeroClass.zero_mul, map_eq_zero_iff M]
 #align is_localization.mk'_eq_zero_iff IsLocalization.mk'_eq_zero_iff
+-/
 
+#print IsLocalization.mk'_zero /-
 @[simp]
 theorem mk'_zero (s : M) : IsLocalization.mk' S 0 s = 0 := by
   rw [eq_comm, IsLocalization.eq_mk'_iff_mul_eq, MulZeroClass.zero_mul, map_zero]
 #align is_localization.mk'_zero IsLocalization.mk'_zero
+-/
 
+#print IsLocalization.ne_zero_of_mk'_ne_zero /-
 theorem ne_zero_of_mk'_ne_zero {x : R} {y : M} (hxy : IsLocalization.mk' S x y ≠ 0) : x ≠ 0 :=
   by
   rintro rfl
   exact hxy (IsLocalization.mk'_zero _)
 #align is_localization.ne_zero_of_mk'_ne_zero IsLocalization.ne_zero_of_mk'_ne_zero
+-/
 
 section Ext
 
 variable [Algebra R P] [IsLocalization M P]
 
+#print IsLocalization.eq_iff_eq /-
 theorem eq_iff_eq {x y} :
     algebraMap R S x = algebraMap R S y ↔ algebraMap R P x = algebraMap R P y :=
   (toLocalizationMap M S).eq_iff_eq (toLocalizationMap M P)
 #align is_localization.eq_iff_eq IsLocalization.eq_iff_eq
+-/
 
+#print IsLocalization.mk'_eq_iff_mk'_eq /-
 theorem mk'_eq_iff_mk'_eq {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ mk' P x₁ y₁ = mk' P x₂ y₂ :=
   (toLocalizationMap M S).mk'_eq_iff_mk'_eq (toLocalizationMap M P)
 #align is_localization.mk'_eq_iff_mk'_eq IsLocalization.mk'_eq_iff_mk'_eq
+-/
 
+#print IsLocalization.mk'_eq_of_eq /-
 theorem mk'_eq_of_eq {a₁ b₁ : R} {a₂ b₂ : M} (H : ↑a₂ * b₁ = ↑b₂ * a₁) :
     mk' S a₁ a₂ = mk' S b₁ b₂ :=
   (toLocalizationMap M S).mk'_eq_of_eq H
 #align is_localization.mk'_eq_of_eq IsLocalization.mk'_eq_of_eq
+-/
 
+#print IsLocalization.mk'_eq_of_eq' /-
 theorem mk'_eq_of_eq' {a₁ b₁ : R} {a₂ b₂ : M} (H : b₁ * ↑a₂ = a₁ * ↑b₂) :
     mk' S a₁ a₂ = mk' S b₁ b₂ :=
   (toLocalizationMap M S).mk'_eq_of_eq' H
 #align is_localization.mk'_eq_of_eq' IsLocalization.mk'_eq_of_eq'
+-/
 
 variable (S)
 
+#print IsLocalization.mk'_self /-
 @[simp]
 theorem mk'_self {x : R} (hx : x ∈ M) : mk' S x ⟨x, hx⟩ = 1 :=
   (toLocalizationMap M S).mk'_self _ hx
 #align is_localization.mk'_self IsLocalization.mk'_self
+-/
 
+#print IsLocalization.mk'_self' /-
 @[simp]
 theorem mk'_self' {x : M} : mk' S (x : R) x = 1 :=
   (toLocalizationMap M S).mk'_self' _
 #align is_localization.mk'_self' IsLocalization.mk'_self'
+-/
 
+#print IsLocalization.mk'_self'' /-
 theorem mk'_self'' {x : M} : mk' S x.1 x = 1 :=
   mk'_self' _
 #align is_localization.mk'_self'' IsLocalization.mk'_self''
+-/
 
 end Ext
 
+#print IsLocalization.mul_mk'_eq_mk'_of_mul /-
 theorem mul_mk'_eq_mk'_of_mul (x y : R) (z : M) :
     (algebraMap R S) x * mk' S y z = mk' S (x * y) z :=
   (toLocalizationMap M S).mul_mk'_eq_mk'_of_mul _ _ _
 #align is_localization.mul_mk'_eq_mk'_of_mul IsLocalization.mul_mk'_eq_mk'_of_mul
+-/
 
+#print IsLocalization.mk'_eq_mul_mk'_one /-
 theorem mk'_eq_mul_mk'_one (x : R) (y : M) : mk' S x y = (algebraMap R S) x * mk' S 1 y :=
   ((toLocalizationMap M S).mul_mk'_one_eq_mk' _ _).symm
 #align is_localization.mk'_eq_mul_mk'_one IsLocalization.mk'_eq_mul_mk'_one
+-/
 
+#print IsLocalization.mk'_mul_cancel_left /-
 @[simp]
 theorem mk'_mul_cancel_left (x : R) (y : M) : mk' S (y * x : R) y = (algebraMap R S) x :=
   (toLocalizationMap M S).mk'_mul_cancel_left _ _
 #align is_localization.mk'_mul_cancel_left IsLocalization.mk'_mul_cancel_left
+-/
 
+#print IsLocalization.mk'_mul_cancel_right /-
 theorem mk'_mul_cancel_right (x : R) (y : M) : mk' S (x * y) y = (algebraMap R S) x :=
   (toLocalizationMap M S).mk'_mul_cancel_right _ _
 #align is_localization.mk'_mul_cancel_right IsLocalization.mk'_mul_cancel_right
+-/
 
+#print IsLocalization.mk'_mul_mk'_eq_one /-
 @[simp]
 theorem mk'_mul_mk'_eq_one (x y : M) : mk' S (x : R) y * mk' S (y : R) x = 1 := by
   rw [← mk'_mul, mul_comm] <;> exact mk'_self _ _
 #align is_localization.mk'_mul_mk'_eq_one IsLocalization.mk'_mul_mk'_eq_one
+-/
 
+#print IsLocalization.mk'_mul_mk'_eq_one' /-
 theorem mk'_mul_mk'_eq_one' (x : R) (y : M) (h : x ∈ M) : mk' S x y * mk' S (y : R) ⟨x, h⟩ = 1 :=
   mk'_mul_mk'_eq_one ⟨x, h⟩ _
 #align is_localization.mk'_mul_mk'_eq_one' IsLocalization.mk'_mul_mk'_eq_one'
+-/
 
 section
 
 variable (M)
 
+#print IsLocalization.isUnit_comp /-
 theorem isUnit_comp (j : S →+* P) (y : M) : IsUnit (j.comp (algebraMap R S) y) :=
   (toLocalizationMap M S).isUnit_comp j.toMonoidHom _
 #align is_localization.is_unit_comp IsLocalization.isUnit_comp
+-/
 
 end
 
+#print IsLocalization.eq_of_eq /-
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g(M) ⊆ units P`, `f x = f y → g x = g y` for all `x y : R`. -/
 theorem eq_of_eq {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) {x y}
     (h : (algebraMap R S) x = (algebraMap R S) y) : g x = g y :=
   @Submonoid.LocalizationMap.eq_of_eq _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom hg _ _ h
 #align is_localization.eq_of_eq IsLocalization.eq_of_eq
+-/
 
+#print IsLocalization.mk'_add /-
 theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
     mk' S (x₁ * y₂ + x₂ * y₁) (y₁ * y₂) = mk' S x₁ y₁ + mk' S x₂ y₂ :=
   mk'_eq_iff_eq_mul.2 <|
@@ -459,7 +546,9 @@ theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
         simp only [map_add, Submonoid.coe_mul, map_mul]
         ring)
 #align is_localization.mk'_add IsLocalization.mk'_add
+-/
 
+#print IsLocalization.mul_add_inv_left /-
 theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (w z₁ z₂ : P) :
     w * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) h y)⁻¹ + z₁ = z₂ ↔ w + g y * z₁ = g y * z₂ :=
   by
@@ -468,7 +557,9 @@ theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (
     IsUnit.coe_liftRight]
   simp only [RingHom.toMonoidHom_eq_coe, MonoidHom.restrict_apply, RingHom.coe_monoidHom]
 #align is_localization.mul_add_inv_left IsLocalization.mul_add_inv_left
+-/
 
+#print IsLocalization.lift_spec_mul_add /-
 theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w' v) :
     ((toLocalizationWithZeroMap M S).lift g.toMonoidWithZeroHom hg) z * w + w' = v ↔
       g ((toLocalizationMap M S).sec z).1 * w + g ((toLocalizationMap M S).sec z).2 * w' =
@@ -478,7 +569,9 @@ theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w'
   erw [mul_comm, ← mul_assoc, mul_add_inv_left hg, mul_comm]
   rfl
 #align is_localization.lift_spec_mul_add IsLocalization.lift_spec_mul_add
+-/
 
+#print IsLocalization.lift /-
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
 `S` to `P` sending `z : S` to `g x * (g y)⁻¹`, where `(x, y) : R × M` are such that
@@ -498,9 +591,11 @@ noncomputable def lift {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) : S →+*
       simp only [sec_spec', to_localization_map_sec, map_add, map_mul]
       ring }
 #align is_localization.lift IsLocalization.lift
+-/
 
 variable {g : R →+* P} (hg : ∀ y : M, IsUnit (g y))
 
+#print IsLocalization.lift_mk' /-
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
 `S` to `P` maps `f x * (f y)⁻¹` to `g x * (g y)⁻¹` for all `x : R, y ∈ M`. -/
@@ -508,45 +603,61 @@ theorem lift_mk' (x y) :
     lift hg (mk' S x y) = g x * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) hg y)⁻¹ :=
   (toLocalizationMap M S).lift_mk' _ _ _
 #align is_localization.lift_mk' IsLocalization.lift_mk'
+-/
 
+#print IsLocalization.lift_mk'_spec /-
 theorem lift_mk'_spec (x v) (y : M) : lift hg (mk' S x y) = v ↔ g x = g y * v :=
   (toLocalizationMap M S).lift_mk'_spec _ _ _ _
 #align is_localization.lift_mk'_spec IsLocalization.lift_mk'_spec
+-/
 
+#print IsLocalization.lift_eq /-
 @[simp]
 theorem lift_eq (x : R) : lift hg ((algebraMap R S) x) = g x :=
   (toLocalizationMap M S).liftEq _ _
 #align is_localization.lift_eq IsLocalization.lift_eq
+-/
 
+#print IsLocalization.lift_eq_iff /-
 theorem lift_eq_iff {x y : R × M} :
     lift hg (mk' S x.1 x.2) = lift hg (mk' S y.1 y.2) ↔ g (x.1 * y.2) = g (y.1 * x.2) :=
   (toLocalizationMap M S).lift_eq_iff _
 #align is_localization.lift_eq_iff IsLocalization.lift_eq_iff
+-/
 
+#print IsLocalization.lift_comp /-
 @[simp]
 theorem lift_comp : (lift hg).comp (algebraMap R S) = g :=
   RingHom.ext <| MonoidHom.ext_iff.1 <| (toLocalizationMap M S).lift_comp _
 #align is_localization.lift_comp IsLocalization.lift_comp
+-/
 
+#print IsLocalization.lift_of_comp /-
 @[simp]
 theorem lift_of_comp (j : S →+* P) : lift (isUnit_comp M j) = j :=
   RingHom.ext <| MonoidHom.ext_iff.1 <| (toLocalizationMap M S).lift_of_comp j.toMonoidHom
 #align is_localization.lift_of_comp IsLocalization.lift_of_comp
+-/
 
 variable (M)
 
+#print IsLocalization.monoidHom_ext /-
 /-- See note [partially-applied ext lemmas] -/
 theorem monoidHom_ext ⦃j k : S →* P⦄
     (h : j.comp (algebraMap R S : R →* S) = k.comp (algebraMap R S)) : j = k :=
   Submonoid.LocalizationMap.epic_of_localizationMap (toLocalizationMap M S) <| MonoidHom.congr_fun h
 #align is_localization.monoid_hom_ext IsLocalization.monoidHom_ext
+-/
 
+#print IsLocalization.ringHom_ext /-
 /-- See note [partially-applied ext lemmas] -/
 theorem ringHom_ext ⦃j k : S →+* P⦄ (h : j.comp (algebraMap R S) = k.comp (algebraMap R S)) :
     j = k :=
   RingHom.coe_monoidHom_injective <| monoidHom_ext M <| MonoidHom.ext <| RingHom.congr_fun h
 #align is_localization.ring_hom_ext IsLocalization.ringHom_ext
+-/
 
+#print IsLocalization.algHom_subsingleton /-
 /- This is not an instance because the submonoid `M` would become a metavariable
   in typeclass search. -/
 theorem algHom_subsingleton [Algebra R P] : Subsingleton (S →ₐ[R] P) :=
@@ -554,7 +665,9 @@ theorem algHom_subsingleton [Algebra R P] : Subsingleton (S →ₐ[R] P) :=
     AlgHom.coe_ringHom_injective <|
       IsLocalization.ringHom_ext M <| by rw [f.comp_algebra_map, g.comp_algebra_map]⟩
 #align is_localization.alg_hom_subsingleton IsLocalization.algHom_subsingleton
+-/
 
+#print IsLocalization.ext /-
 /-- To show `j` and `k` agree on the whole localization, it suffices to show they agree
 on the image of the base ring, if they preserve `1` and `*`. -/
 protected theorem ext (j k : S → P) (hj1 : j 1 = 1) (hk1 : k 1 = 1)
@@ -562,30 +675,39 @@ protected theorem ext (j k : S → P) (hj1 : j 1 = 1) (hk1 : k 1 = 1)
     (h : ∀ a, j (algebraMap R S a) = k (algebraMap R S a)) : j = k :=
   MonoidHom.mk.inj (monoidHom_ext M <| MonoidHom.ext h : (⟨j, hj1, hjm⟩ : S →* P) = ⟨k, hk1, hkm⟩)
 #align is_localization.ext IsLocalization.ext
+-/
 
 variable {M}
 
+#print IsLocalization.lift_unique /-
 theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) : lift hg = j :=
   RingHom.ext <|
     MonoidHom.ext_iff.1 <|
       @Submonoid.LocalizationMap.lift_unique _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom hg
         j.toMonoidHom hj
 #align is_localization.lift_unique IsLocalization.lift_unique
+-/
 
+#print IsLocalization.lift_id /-
 @[simp]
 theorem lift_id (x) : lift (map_units S : ∀ y : M, IsUnit _) x = x :=
   (toLocalizationMap M S).lift_id _
 #align is_localization.lift_id IsLocalization.lift_id
+-/
 
+#print IsLocalization.lift_surjective_iff /-
 theorem lift_surjective_iff :
     Surjective (lift hg : S → P) ↔ ∀ v : P, ∃ x : R × M, v * g x.2 = g x.1 :=
   (toLocalizationMap M S).lift_surjective_iff hg
 #align is_localization.lift_surjective_iff IsLocalization.lift_surjective_iff
+-/
 
+#print IsLocalization.lift_injective_iff /-
 theorem lift_injective_iff :
     Injective (lift hg : S → P) ↔ ∀ x y, algebraMap R S x = algebraMap R S y ↔ g x = g y :=
   (toLocalizationMap M S).lift_injective_iff hg
 #align is_localization.lift_injective_iff IsLocalization.lift_injective_iff
+-/
 
 section Map
 
@@ -597,6 +719,7 @@ section
 
 variable (Q)
 
+#print IsLocalization.map /-
 /-- Map a homomorphism `g : R →+* P` to `S →+* Q`, where `S` and `Q` are
 localizations of `R` and `P` at `M` and `T` respectively,
 such that `g(M) ⊆ T`.
@@ -606,34 +729,46 @@ We send `z : S` to `algebra_map P Q (g x) * (algebra_map P Q (g y))⁻¹`, where
 noncomputable def map (g : R →+* P) (hy : M ≤ T.comap g) : S →+* Q :=
   @lift R _ M _ _ _ _ _ _ ((algebraMap P Q).comp g) fun y => map_units _ ⟨g y, hy y.2⟩
 #align is_localization.map IsLocalization.map
+-/
 
 end
 
+#print IsLocalization.map_eq /-
 theorem map_eq (x) : map Q g hy ((algebraMap R S) x) = algebraMap P Q (g x) :=
   lift_eq (fun y => map_units _ ⟨g y, hy y.2⟩) x
 #align is_localization.map_eq IsLocalization.map_eq
+-/
 
+#print IsLocalization.map_comp /-
 @[simp]
 theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g :=
   lift_comp fun y => map_units _ ⟨g y, hy y.2⟩
 #align is_localization.map_comp IsLocalization.map_comp
+-/
 
+#print IsLocalization.map_mk' /-
 theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.2⟩ :=
   @Submonoid.LocalizationMap.map_mk' _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom _
     (fun y => hy y.2) _ _ (toLocalizationMap T Q) _ _
 #align is_localization.map_mk' IsLocalization.map_mk'
+-/
 
+#print IsLocalization.map_id /-
 @[simp]
 theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
     map S (RingHom.id _) h z = z :=
   lift_id _
 #align is_localization.map_id IsLocalization.map_id
+-/
 
+#print IsLocalization.map_unique /-
 theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algebraMap P Q (g x)) :
     map Q g hy = j :=
   lift_unique (fun y => map_units _ ⟨g y, hy y.2⟩) hj
 #align is_localization.map_unique IsLocalization.map_unique
+-/
 
+#print IsLocalization.map_comp_map /-
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
 theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W]
@@ -643,7 +778,9 @@ theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSe
     @Submonoid.LocalizationMap.map_map _ _ _ _ _ P _ (toLocalizationMap M S) g _ _ _ _ _ _ _ _ _ _
       (toLocalizationMap U W) l _ x
 #align is_localization.map_comp_map IsLocalization.map_comp_map
+-/
 
+#print IsLocalization.map_map /-
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
 theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W] [Algebra A W]
@@ -651,15 +788,19 @@ theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemirin
     map W l hl (map Q g hy x) = map W (l.comp g) (fun x hx => hl (hy hx)) x := by
   rw [← map_comp_map hy hl] <;> rfl
 #align is_localization.map_map IsLocalization.map_map
+-/
 
+#print IsLocalization.map_smul /-
 theorem map_smul (x : S) (z : R) : map Q g hy (z • x : S) = g z • map Q g hy x := by
   rw [Algebra.smul_def, Algebra.smul_def, RingHom.map_mul, map_eq]
 #align is_localization.map_smul IsLocalization.map_smul
+-/
 
 section
 
 variable (S Q)
 
+#print IsLocalization.ringEquivOfRingEquiv /-
 /-- If `S`, `Q` are localizations of `R` and `P` at submonoids `M, T` respectively, an
 isomorphism `j : R ≃+* P` such that `j(M) = T` induces an isomorphism of localizations
 `S ≃+* Q`. -/
@@ -681,26 +822,33 @@ noncomputable def ringEquivOfRingEquiv (h : R ≃+* P) (H : M.map h.toMonoidHom
       rw [map_map, map_unique _ (RingHom.id _), RingHom.id_apply]
       intro x; convert congr_arg (algebraMap P Q) (h.apply_symm_apply x).symm }
 #align is_localization.ring_equiv_of_ring_equiv IsLocalization.ringEquivOfRingEquiv
+-/
 
 end
 
+#print IsLocalization.ringEquivOfRingEquiv_eq_map /-
 theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T) :
     (ringEquivOfRingEquiv S Q j H : S →+* Q) =
       map Q (j : R →+* P) (M.le_comap_of_map_le (le_of_eq H)) :=
   rfl
 #align is_localization.ring_equiv_of_ring_equiv_eq_map IsLocalization.ringEquivOfRingEquiv_eq_map
+-/
 
+#print IsLocalization.ringEquivOfRingEquiv_eq /-
 @[simp]
 theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x) :
     ringEquivOfRingEquiv S Q j H ((algebraMap R S) x) = algebraMap P Q (j x) :=
   map_eq _ _
 #align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eq
+-/
 
+#print IsLocalization.ringEquivOfRingEquiv_mk' /-
 theorem ringEquivOfRingEquiv_mk' {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x : R) (y : M) :
     ringEquivOfRingEquiv S Q j H (mk' S x y) =
       mk' Q (j x) ⟨j y, show j y ∈ T from H ▸ Set.mem_image_of_mem j y.2⟩ :=
   map_mk' _ _ _
 #align is_localization.ring_equiv_of_ring_equiv_mk' IsLocalization.ringEquivOfRingEquiv_mk'
+-/
 
 end Map
 
@@ -724,15 +872,19 @@ noncomputable def algEquiv : S ≃ₐ[R] Q :=
 
 end
 
+#print IsLocalization.algEquiv_mk' /-
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
   map_mk' _ _ _
 #align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'
+-/
 
+#print IsLocalization.algEquiv_symm_mk' /-
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) = mk' S x y :=
   map_mk' _ _ _
 #align is_localization.alg_equiv_symm_mk' IsLocalization.algEquiv_symm_mk'
+-/
 
 end AlgEquiv
 
@@ -742,6 +894,7 @@ section
 
 variable (M)
 
+#print IsLocalization.isLocalization_of_algEquiv /-
 theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃ₐ[R] P) :
     IsLocalization M P := by
   constructor
@@ -758,20 +911,26 @@ theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃
       h.symm.commutes]
     rfl
 #align is_localization.is_localization_of_alg_equiv IsLocalization.isLocalization_of_algEquiv
+-/
 
+#print IsLocalization.isLocalization_iff_of_algEquiv /-
 theorem isLocalization_iff_of_algEquiv [Algebra R P] (h : S ≃ₐ[R] P) :
     IsLocalization M S ↔ IsLocalization M P :=
   ⟨fun _ => is_localization_of_alg_equiv M h, fun _ => is_localization_of_alg_equiv M h.symm⟩
 #align is_localization.is_localization_iff_of_alg_equiv IsLocalization.isLocalization_iff_of_algEquiv
+-/
 
+#print IsLocalization.isLocalization_iff_of_ringEquiv /-
 theorem isLocalization_iff_of_ringEquiv (h : S ≃+* P) :
     IsLocalization M S ↔ @IsLocalization _ M P _ (h.toRingHom.comp <| algebraMap R S).toAlgebra :=
   letI := (h.to_ring_hom.comp <| algebraMap R S).toAlgebra
   is_localization_iff_of_alg_equiv M { h with commutes' := fun _ => rfl }
 #align is_localization.is_localization_iff_of_ring_equiv IsLocalization.isLocalization_iff_of_ringEquiv
+-/
 
 variable (S)
 
+#print IsLocalization.isLocalization_of_base_ringEquiv /-
 theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
     @IsLocalization _ (M.map h.toMonoidHom) S _
       ((algebraMap R S).comp h.symm.toRingHom).toAlgebra :=
@@ -795,7 +954,9 @@ theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
     exact
       ⟨fun ⟨c, e⟩ => ⟨⟨_, _, c.Prop, rfl⟩, e⟩, fun ⟨⟨_, c, h, e₁⟩, e₂⟩ => ⟨⟨_, h⟩, e₁.symm ▸ e₂⟩⟩
 #align is_localization.is_localization_of_base_ring_equiv IsLocalization.isLocalization_of_base_ringEquiv
+-/
 
+#print IsLocalization.isLocalization_iff_of_base_ringEquiv /-
 theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
     IsLocalization M S ↔
       @IsLocalization _ (M.map h.toMonoidHom) S _
@@ -813,13 +974,13 @@ theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
   intro r
   rw [RingHom.algebraMap_toAlgebra]
 #align is_localization.is_localization_iff_of_base_ring_equiv IsLocalization.isLocalization_iff_of_base_ringEquiv
+-/
 
 end
 
 variable (M S)
 
-include M
-
+#print IsLocalization.nonZeroDivisors_le_comap /-
 theorem nonZeroDivisors_le_comap [IsLocalization M S] :
     nonZeroDivisors R ≤ (nonZeroDivisors S).comap (algebraMap R S) :=
   by
@@ -832,11 +993,14 @@ theorem nonZeroDivisors_le_comap [IsLocalization M S] :
   rw [mk'_eq_zero_iff]
   exact ⟨c, ha _ e⟩
 #align is_localization.non_zero_divisors_le_comap IsLocalization.nonZeroDivisors_le_comap
+-/
 
+#print IsLocalization.map_nonZeroDivisors_le /-
 theorem map_nonZeroDivisors_le [IsLocalization M S] :
     (nonZeroDivisors R).map (algebraMap R S) ≤ nonZeroDivisors S :=
   Submonoid.map_le_iff_le_comap.mpr (nonZeroDivisors_le_comap M S)
 #align is_localization.map_non_zero_divisors_le IsLocalization.map_nonZeroDivisors_le
+-/
 
 end IsLocalization
 
@@ -881,10 +1045,13 @@ protected irreducible_def add (z w : Localization M) : Localization M :=
 instance : Add (Localization M) :=
   ⟨Localization.add⟩
 
+#print Localization.add_mk /-
 theorem add_mk (a b c d) : (mk a b : Localization M) + mk c d = mk (b * c + d * a) (b * d) := by
   unfold Add.add Localization.add; apply lift_on₂_mk
 #align localization.add_mk Localization.add_mk
+-/
 
+#print Localization.add_mk_self /-
 theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b :=
   by
   rw [add_mk, mk_eq_mk_iff, r_eq_r']
@@ -892,6 +1059,7 @@ theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b
   simp only [Submonoid.coe_one, Submonoid.coe_mul]
   ring
 #align localization.add_mk_self Localization.add_mk_self
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
 private unsafe def tac :=
@@ -946,6 +1114,7 @@ instance : CommSemiring (Localization M) :=
           run_tac
             tac) }
 
+#print Localization.mkAddMonoidHom /-
 /-- For any given denominator `b : M`, the map `a ↦ a / b` is an `add_monoid_hom` from `R` to
   `localization M`-/
 @[simps]
@@ -955,19 +1124,26 @@ def mkAddMonoidHom (b : M) : R →+ Localization M
   map_zero' := mk_zero _
   map_add' x y := (add_mk_self _ _ _).symm
 #align localization.mk_add_monoid_hom Localization.mkAddMonoidHom
+-/
 
+#print Localization.mk_sum /-
 theorem mk_sum {ι : Type _} (f : ι → R) (s : Finset ι) (b : M) :
     mk (∑ i in s, f i) b = ∑ i in s, mk (f i) b :=
   (mkAddMonoidHom b).map_sum f s
 #align localization.mk_sum Localization.mk_sum
+-/
 
+#print Localization.mk_list_sum /-
 theorem mk_list_sum (l : List R) (b : M) : mk l.Sum b = (l.map fun a => mk a b).Sum :=
   (mkAddMonoidHom b).map_list_sum l
 #align localization.mk_list_sum Localization.mk_list_sum
+-/
 
+#print Localization.mk_multiset_sum /-
 theorem mk_multiset_sum (l : Multiset R) (b : M) : mk l.Sum b = (l.map fun a => mk a b).Sum :=
   (mkAddMonoidHom b).map_multiset_sum l
 #align localization.mk_multiset_sum Localization.mk_multiset_sum
+-/
 
 instance {S : Type _} [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] :
     DistribMulAction S (Localization M)
@@ -1027,36 +1203,50 @@ instance : IsLocalization M (Localization M)
 
 end
 
+#print Localization.toLocalizationMap_eq_monoidOf /-
 @[simp]
 theorem toLocalizationMap_eq_monoidOf : toLocalizationMap M (Localization M) = monoidOf M :=
   rfl
 #align localization.to_localization_map_eq_monoid_of Localization.toLocalizationMap_eq_monoidOf
+-/
 
+#print Localization.monoidOf_eq_algebraMap /-
 theorem monoidOf_eq_algebraMap (x) : (monoidOf M).toMap x = algebraMap R (Localization M) x :=
   rfl
 #align localization.monoid_of_eq_algebra_map Localization.monoidOf_eq_algebraMap
+-/
 
+#print Localization.mk_one_eq_algebraMap /-
 theorem mk_one_eq_algebraMap (x) : mk x 1 = algebraMap R (Localization M) x :=
   rfl
 #align localization.mk_one_eq_algebra_map Localization.mk_one_eq_algebraMap
+-/
 
+#print Localization.mk_eq_mk'_apply /-
 theorem mk_eq_mk'_apply (x y) : mk x y = IsLocalization.mk' (Localization M) x y := by
   rw [mk_eq_monoid_of_mk'_apply, mk', to_localization_map_eq_monoid_of]
 #align localization.mk_eq_mk'_apply Localization.mk_eq_mk'_apply
+-/
 
+#print Localization.mk_eq_mk' /-
 @[simp]
 theorem mk_eq_mk' : (mk : R → M → Localization M) = IsLocalization.mk' (Localization M) :=
   mk_eq_monoidOf_mk'
 #align localization.mk_eq_mk' Localization.mk_eq_mk'
+-/
 
+#print Localization.mk_algebraMap /-
 theorem mk_algebraMap {A : Type _} [CommSemiring A] [Algebra A R] (m : A) :
     mk (algebraMap A R m) 1 = algebraMap A (Localization M) m := by
   rw [mk_eq_mk', mk'_eq_iff_eq_mul, Submonoid.coe_one, map_one, mul_one] <;> rfl
 #align localization.mk_algebra_map Localization.mk_algebraMap
+-/
 
+#print Localization.mk_nat_cast /-
 theorem mk_nat_cast (m : ℕ) : (mk m 1 : Localization M) = m := by
   simpa using @mk_algebra_map R _ M ℕ _ _ m
 #align localization.mk_nat_cast Localization.mk_nat_cast
+-/
 
 variable [IsLocalization M S]
 
@@ -1064,11 +1254,13 @@ section
 
 variable (M S)
 
+#print Localization.algEquiv /-
 /-- The localization of `R` at `M` as a quotient type is isomorphic to any other localization. -/
 @[simps]
 noncomputable def algEquiv : Localization M ≃ₐ[R] S :=
   IsLocalization.algEquiv M _ _
 #align localization.alg_equiv Localization.algEquiv
+-/
 
 #print IsLocalization.unique /-
 /-- The localization of a singleton is a singleton. Cannot be an instance due to metavariables. -/
@@ -1081,23 +1273,31 @@ noncomputable def IsLocalization.unique (R Rₘ) [CommSemiring R] [CommSemiring
 
 end
 
+#print Localization.algEquiv_mk' /-
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) = mk' S x y :=
   algEquiv_mk' _ _
 #align localization.alg_equiv_mk' Localization.algEquiv_mk'
+-/
 
+#print Localization.algEquiv_symm_mk' /-
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) :
     (algEquiv M S).symm (mk' S x y) = mk' (Localization M) x y :=
   algEquiv_symm_mk' _ _
 #align localization.alg_equiv_symm_mk' Localization.algEquiv_symm_mk'
+-/
 
+#print Localization.algEquiv_mk /-
 theorem algEquiv_mk (x y) : algEquiv M S (mk x y) = mk' S x y := by rw [mk_eq_mk', alg_equiv_mk']
 #align localization.alg_equiv_mk Localization.algEquiv_mk
+-/
 
+#print Localization.algEquiv_symm_mk /-
 theorem algEquiv_symm_mk (x : R) (y : M) : (algEquiv M S).symm (mk' S x y) = mk x y := by
   rw [mk_eq_mk', alg_equiv_symm_mk']
 #align localization.alg_equiv_symm_mk Localization.algEquiv_symm_mk
+-/
 
 end Localization
 
@@ -1128,9 +1328,11 @@ protected irreducible_def neg (z : Localization M) : Localization M :=
 instance : Neg (Localization M) :=
   ⟨Localization.neg⟩
 
+#print Localization.neg_mk /-
 theorem neg_mk (a b) : -(mk a b : Localization M) = mk (-a) b := by unfold Neg.neg Localization.neg;
   apply lift_on_mk
 #align localization.neg_mk Localization.neg_mk
+-/
 
 instance : CommRing (Localization M) :=
   { Localization.commSemiring with
@@ -1154,6 +1356,7 @@ instance : CommRing (Localization M) :=
           simp only [Submonoid.coe_mul]
           ring) }
 
+#print Localization.sub_mk /-
 theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b * c) (b * d) :=
   calc
     mk a b - mk c d = mk a b + -mk c d := sub_eq_add_neg _ _
@@ -1161,10 +1364,13 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b
     _ = mk (b * -c + d * a) (b * d) := (add_mk _ _ _ _)
     _ = mk (d * a - b * c) (b * d) := by congr <;> ring
 #align localization.sub_mk Localization.sub_mk
+-/
 
+#print Localization.mk_int_cast /-
 theorem mk_int_cast (m : ℤ) : (mk m 1 : Localization M) = m := by
   simpa using @mk_algebra_map R _ M ℤ _ _ m
 #align localization.mk_int_cast Localization.mk_int_cast
+-/
 
 end Localization
 
@@ -1172,6 +1378,7 @@ namespace IsLocalization
 
 variable {R M} (S) {K : Type _} [IsLocalization M S]
 
+#print IsLocalization.to_map_eq_zero_iff /-
 theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R S x = 0 ↔ x = 0 :=
   by
   rw [← (algebraMap R S).map_zero]
@@ -1181,27 +1388,35 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
     exact hM c.2 x hc
   · rw [h]
 #align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iff
+-/
 
+#print IsLocalization.injective /-
 protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraMap R S) :=
   by
   rw [injective_iff_map_eq_zero (algebraMap R S)]
   intro a ha
   rwa [to_map_eq_zero_iff S hM] at ha 
 #align is_localization.injective IsLocalization.injective
+-/
 
+#print IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisors /-
 protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M ≤ nonZeroDivisors R)
     {x : R} (hx : x ∈ nonZeroDivisors R) : algebraMap R S x ≠ 0 :=
   show (algebraMap R S).toMonoidWithZeroHom x ≠ 0 from
     map_ne_zero_of_mem_nonZeroDivisors (algebraMap R S) (IsLocalization.injective S hM) hx
 #align is_localization.to_map_ne_zero_of_mem_non_zero_divisors IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisors
+-/
 
 variable {S}
 
+#print IsLocalization.sec_snd_ne_zero /-
 theorem sec_snd_ne_zero [Nontrivial R] (hM : M ≤ nonZeroDivisors R) (x : S) :
     ((sec M x).snd : R) ≠ 0 :=
   nonZeroDivisors.coe_ne_zero ⟨(sec M x).snd.val, hM (sec M x).snd.property⟩
 #align is_localization.sec_snd_ne_zero IsLocalization.sec_snd_ne_zero
+-/
 
+#print IsLocalization.sec_fst_ne_zero /-
 theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDivisors R) {x : S}
     (hx : x ≠ 0) : (sec M x).fst ≠ 0 :=
   by
@@ -1211,9 +1426,11 @@ theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDiv
   · exact Or.elim hsec hx (sec_snd_ne_zero hM x)
   · exact IsLocalization.injective S hM
 #align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zero
+-/
 
 variable (S M) (Q : Type _) [CommRing Q] {g : R →+* P} [Algebra P Q]
 
+#print IsLocalization.map_injective_of_injective /-
 /-- Injectivity of a map descends to the map induced on localizations. -/
 theorem map_injective_of_injective (hg : Function.Injective g)
     [IsLocalization (M.map g : Submonoid P) Q] :
@@ -1230,11 +1447,13 @@ theorem map_injective_of_injective (hg : Function.Injective g)
   rw [mk'_eq_zero_iff]
   exact ⟨⟨n, hn⟩, hg hm⟩
 #align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injective
+-/
 
 variable {S Q M}
 
 variable (A : Type _) [CommRing A] [IsDomain A]
 
+#print IsLocalization.noZeroDivisors_of_le_nonZeroDivisors /-
 /-- A `comm_ring` `S` which is the localization of a ring `R` without zero divisors at a subset of
 non-zero elements does not have zero divisors.
 See note [reducible non-instances]. -/
@@ -1254,7 +1473,9 @@ theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [Is
       · exact Or.inl (eq_zero_of_fst_eq_zero hx H)
       · exact Or.inr (eq_zero_of_fst_eq_zero hy H) }
 #align is_localization.no_zero_divisors_of_le_non_zero_divisors IsLocalization.noZeroDivisors_of_le_nonZeroDivisors
+-/
 
+#print IsLocalization.isDomain_of_le_nonZeroDivisors /-
 /-- A `comm_ring` `S` which is the localization of an integral domain `R` at a subset of
 non-zero elements is an integral domain.
 See note [reducible non-instances]. -/
@@ -1269,9 +1490,11 @@ theorem isDomain_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [IsLocali
           zero_ne_one (IsLocalization.injective S hM h)⟩⟩
   · exact no_zero_divisors_of_le_non_zero_divisors _ hM
 #align is_localization.is_domain_of_le_non_zero_divisors IsLocalization.isDomain_of_le_nonZeroDivisors
+-/
 
 variable {A}
 
+#print IsLocalization.isDomain_localization /-
 /-- The localization at of an integral domain to a set of non-zero elements is an integral domain.
 See note [reducible non-instances]. -/
 @[reducible]
@@ -1279,11 +1502,13 @@ theorem isDomain_localization {M : Submonoid A} (hM : M ≤ nonZeroDivisors A) :
     IsDomain (Localization M) :=
   isDomain_of_le_nonZeroDivisors _ hM
 #align is_localization.is_domain_localization IsLocalization.isDomain_localization
+-/
 
 end IsLocalization
 
 open IsLocalization
 
+#print IsField.localization_map_bijective /-
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommRing Rₘ]
     {M : Submonoid R} (hM : (0 : R) ∉ M) (hR : IsField R) [Algebra R Rₘ] [IsLocalization M Rₘ] :
@@ -1296,13 +1521,16 @@ theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommR
   obtain ⟨n, hn⟩ := hR.mul_inv_cancel (nonZeroDivisors.ne_zero <| hM hm)
   exact ⟨r * n, by erw [eq_mk'_iff_mul_eq, ← map_mul, mul_assoc, mul_comm n, hn, mul_one]⟩
 #align is_field.localization_map_bijective IsField.localization_map_bijective
+-/
 
+#print Field.localization_map_bijective /-
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem Field.localization_map_bijective {K Kₘ : Type _} [Field K] [CommRing Kₘ] {M : Submonoid K}
     (hM : (0 : K) ∉ M) [Algebra K Kₘ] [IsLocalization M Kₘ] :
     Function.Bijective (algebraMap K Kₘ) :=
   (Field.toIsField K).localization_map_bijective hM
 #align field.localization_map_bijective Field.localization_map_bijective
+-/
 
 -- this looks weird due to the `letI` inside the above lemma, but trying to do it the other
 -- way round causes issues with defeq of instances, so this is actually easier.
@@ -1344,14 +1572,15 @@ variable [Algebra Rₘ Sₘ] [Algebra R Sₘ] [IsScalarTower R Rₘ Sₘ] [IsSca
 
 variable (S Rₘ Sₘ)
 
-include S
-
+#print IsLocalization.map_units_map_submonoid /-
 theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R Sₘ y) :=
   by
   rw [IsScalarTower.algebraMap_apply _ S]
   exact IsLocalization.map_units Sₘ ⟨algebraMap R S y, Algebra.mem_algebraMapSubmonoid_of_mem y⟩
 #align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoid
+-/
 
+#print IsLocalization.algebraMap_mk' /-
 @[simp]
 theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
     algebraMap Rₘ Sₘ (IsLocalization.mk' Rₘ x y) =
@@ -1364,9 +1593,11 @@ theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
     IsLocalization.mul_mk'_eq_mk'_of_mul]
   exact congr_arg (algebraMap Rₘ Sₘ) (IsLocalization.mk'_mul_cancel_left x y)
 #align is_localization.algebra_map_mk' IsLocalization.algebraMap_mk'
+-/
 
 variable (M)
 
+#print IsLocalization.algebraMap_eq_map_map_submonoid /-
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
 R  →  S
@@ -1382,7 +1613,9 @@ theorem IsLocalization.algebraMap_eq_map_map_submonoid :
     IsLocalization.map_unique _ (algebraMap Rₘ Sₘ) fun x => by
       rw [← IsScalarTower.algebraMap_apply R S Sₘ, ← IsScalarTower.algebraMap_apply R Rₘ Sₘ]
 #align is_localization.algebra_map_eq_map_map_submonoid IsLocalization.algebraMap_eq_map_map_submonoid
+-/
 
+#print IsLocalization.algebraMap_apply_eq_map_map_submonoid /-
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
 R  →  S
@@ -1396,25 +1629,30 @@ theorem IsLocalization.algebraMap_apply_eq_map_map_submonoid (x) :
         (show _ ≤ (Algebra.algebraMapSubmonoid S M).comap _ from M.le_comap_map) x :=
   FunLike.congr_fun (IsLocalization.algebraMap_eq_map_map_submonoid _ _ _ _) x
 #align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoid
+-/
 
 variable {R}
 
+#print IsLocalization.lift_algebraMap_eq_algebraMap /-
 theorem IsLocalization.lift_algebraMap_eq_algebraMap :
     @IsLocalization.lift R _ M Rₘ _ _ Sₘ _ _ (algebraMap R Sₘ)
         (IsLocalization.map_units_map_submonoid S Sₘ) =
       algebraMap Rₘ Sₘ :=
   IsLocalization.lift_unique _ fun x => (IsScalarTower.algebraMap_apply _ _ _ _).symm
 #align is_localization.lift_algebra_map_eq_algebra_map IsLocalization.lift_algebraMap_eq_algebraMap
+-/
 
 end
 
 variable (Rₘ Sₘ)
 
+#print localizationAlgebra_injective /-
 /-- Injectivity of the underlying `algebra_map` descends to the algebra induced by localization. -/
 theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)) :
     Function.Injective (@algebraMap Rₘ Sₘ _ _ (localizationAlgebra M S)) :=
   IsLocalization.map_injective_of_injective M Rₘ Sₘ hRS
 #align localization_algebra_injective localizationAlgebra_injective
+-/
 
 end Algebra
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -874,8 +874,7 @@ protected irreducible_def add (z w : Localization M) : Localization M :=
           ↑t₅ * ↑t₆ * (↑b' * ↑d' * ((b : R) * c + d * a)) =
               t₆ * (d' * c) * (t₅ * (b' * b)) + t₅ * (b' * a) * (t₆ * (d' * d)) :=
             by ring
-          _ = t₅ * t₆ * (b * d * (b' * c' + d' * a')) := by rw [ht₆, ht₅] <;> ring
-          )
+          _ = t₅ * t₆ * (b * d * (b' * c' + d' * a')) := by rw [ht₆, ht₅] <;> ring)
 #align localization.add Localization.add
 -/
 
@@ -894,7 +893,7 @@ theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b
   ring
 #align localization.add_mk_self Localization.add_mk_self
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
 private unsafe def tac :=
   sorry
 
@@ -1161,7 +1160,6 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b
     _ = mk a b + mk (-c) d := by rw [neg_mk]
     _ = mk (b * -c + d * a) (b * d) := (add_mk _ _ _ _)
     _ = mk (d * a - b * c) (b * d) := by congr <;> ring
-    
 #align localization.sub_mk Localization.sub_mk
 
 theorem mk_int_cast (m : ℤ) : (mk m 1 : Localization M) = m := by

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

@@ -101,9 +101,9 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 variable [Algebra R S] {P : Type _} [CommSemiring P]
 
 #print IsLocalization /-
-/- ./././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 typeclass `is_localization (M : submodule R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
 class IsLocalization : Prop where
@@ -746,11 +746,11 @@ theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃
     IsLocalization M P := by
   constructor
   · intro y
-    convert(IsLocalization.map_units S y).map h.to_alg_hom.to_ring_hom.to_monoid_hom
+    convert (IsLocalization.map_units S y).map h.to_alg_hom.to_ring_hom.to_monoid_hom
     exact (h.commutes y).symm
   · intro y
     obtain ⟨⟨x, s⟩, e⟩ := IsLocalization.surj M (h.symm y)
-    apply_fun h  at e 
+    apply_fun h at e 
     simp only [h.map_mul, h.apply_symm_apply, h.commutes] at e 
     exact ⟨⟨x, s⟩, e⟩
   · intro x y
@@ -804,7 +804,7 @@ theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
   refine' ⟨fun _ => is_localization_of_base_ring_equiv _ _ h, _⟩
   letI := ((algebraMap R S).comp h.symm.to_ring_hom).toAlgebra
   intro H
-  convert@is_localization_of_base_ring_equiv _ _ _ _ _ _ H h.symm
+  convert @is_localization_of_base_ring_equiv _ _ _ _ _ _ H h.symm
   · erw [Submonoid.map_equiv_eq_comap_symm, Submonoid.comap_map_eq_of_injective]
     exact h.to_equiv.injective
   rw [RingHom.algebraMap_toAlgebra, RingHom.comp_assoc]

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

@@ -213,7 +213,7 @@ theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R
 
 theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebraMap R S x)
     (hx : x = 0) : z = 0 := by
-  rw [hx, (algebraMap R S).map_zero] at h
+  rw [hx, (algebraMap R S).map_zero] at h 
   exact (IsUnit.mul_left_eq_zero (IsLocalization.map_units S y)).1 h
 #align is_localization.eq_zero_of_fst_eq_zero IsLocalization.eq_zero_of_fst_eq_zero
 
@@ -294,7 +294,7 @@ theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
 
 variable (M)
 
-theorem mk'_surjective (z : S) : ∃ (x : _)(y : M), mk' S x y = z :=
+theorem mk'_surjective (z : S) : ∃ (x : _) (y : M), mk' S x y = z :=
   let ⟨r, hr⟩ := IsLocalization.surj _ z
   ⟨r.1, r.2, (eq_mk'_iff_mul_eq.2 hr).symm⟩
 #align is_localization.mk'_surjective IsLocalization.mk'_surjective
@@ -336,10 +336,10 @@ theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R
   constructor <;> intro h
   · rw [← mk'_spec S x y, mul_comm]
     exact I.mul_mem_left ((algebraMap R S) y) h
-  · rw [← mk'_spec S x y] at h
+  · rw [← mk'_spec S x y] at h 
     obtain ⟨b, hb⟩ := isUnit_iff_exists_inv.1 (map_units S y)
     have := I.mul_mem_left b h
-    rwa [mul_comm, mul_assoc, hb, mul_one] at this
+    rwa [mul_comm, mul_assoc, hb, mul_one] at this 
 #align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iff
 
 protected theorem eq {a₁ b₁} {a₂ b₂ : M} :
@@ -665,7 +665,7 @@ isomorphism `j : R ≃+* P` such that `j(M) = T` induces an isomorphism of local
 `S ≃+* Q`. -/
 @[simps]
 noncomputable def ringEquivOfRingEquiv (h : R ≃+* P) (H : M.map h.toMonoidHom = T) : S ≃+* Q :=
-  have H' : T.map h.symm.toMonoidHom = M := by rw [← M.map_id, ← H, Submonoid.map_map]; congr ; ext;
+  have H' : T.map h.symm.toMonoidHom = M := by rw [← M.map_id, ← H, Submonoid.map_map]; congr; ext;
     apply h.symm_apply_apply
   {
     map Q (h : R →+* P)
@@ -750,8 +750,8 @@ theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃
     exact (h.commutes y).symm
   · intro y
     obtain ⟨⟨x, s⟩, e⟩ := IsLocalization.surj M (h.symm y)
-    apply_fun h  at e
-    simp only [h.map_mul, h.apply_symm_apply, h.commutes] at e
+    apply_fun h  at e 
+    simp only [h.map_mul, h.apply_symm_apply, h.commutes] at e 
     exact ⟨⟨x, s⟩, e⟩
   · intro x y
     rw [← h.symm.to_equiv.injective.eq_iff, ← IsLocalization.eq_iff_exists M S, ← h.symm.commutes, ←
@@ -784,7 +784,7 @@ theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
   · intro y
     obtain ⟨⟨x, s⟩, e⟩ := IsLocalization.surj M y
     refine' ⟨⟨h x, _, _, s.prop, rfl⟩, _⟩
-    dsimp only [RingHom.algebraMap_toAlgebra, RingHom.comp_apply] at e⊢
+    dsimp only [RingHom.algebraMap_toAlgebra, RingHom.comp_apply] at e ⊢
     convert e <;> exact h.symm_apply_apply _
   · intro x y
     rw [RingHom.algebraMap_toAlgebra, RingHom.comp_apply, RingHom.comp_apply,
@@ -826,9 +826,9 @@ theorem nonZeroDivisors_le_comap [IsLocalization M S] :
   rintro a ha b (e : b * algebraMap R S a = 0)
   obtain ⟨x, s, rfl⟩ := mk'_surjective M b
   rw [← @mk'_one R _ M, ← mk'_mul, ← (algebraMap R S).map_zero, ← @mk'_one R _ M,
-    IsLocalization.eq] at e
+    IsLocalization.eq] at e 
   obtain ⟨c, e⟩ := e
-  rw [MulZeroClass.mul_zero, MulZeroClass.mul_zero, Submonoid.coe_one, one_mul, ← mul_assoc] at e
+  rw [MulZeroClass.mul_zero, MulZeroClass.mul_zero, Submonoid.coe_one, one_mul, ← mul_assoc] at e 
   rw [mk'_eq_zero_iff]
   exact ⟨c, ha _ e⟩
 #align is_localization.non_zero_divisors_le_comap IsLocalization.nonZeroDivisors_le_comap
@@ -852,7 +852,7 @@ variable {M}
 section
 
 instance [Subsingleton R] : Unique (Localization M) :=
-  ⟨⟨1⟩, by intro a; induction a; induction default; congr ; rfl; rfl⟩
+  ⟨⟨1⟩, by intro a; induction a; induction default; congr; rfl; rfl⟩
 
 #print Localization.add /-
 /-- Addition in a ring localization is defined as `⟨a, b⟩ + ⟨c, d⟩ = ⟨b * c + d * a, b * d⟩`.
@@ -865,7 +865,7 @@ protected irreducible_def add (z w : Localization M) : Localization M :=
     fun a a' b b' c c' d d' h1 h2 =>
     mk_eq_mk_iff.2
       (by
-        rw [r_eq_r'] at h1 h2⊢
+        rw [r_eq_r'] at h1 h2 ⊢
         cases' h1 with t₅ ht₅
         cases' h2 with t₆ ht₆
         use t₅ * t₆
@@ -990,10 +990,10 @@ instance {S : Type _} [Semiring S] [Module S R] [IsScalarTower S R R] : Module S
     Localization.distribMulAction with
     zero_smul :=
       Localization.ind <|
-        Prod.rec <| by intros ; simp only [Localization.smul_mk, zero_smul, mk_zero]
+        Prod.rec <| by intros; simp only [Localization.smul_mk, zero_smul, mk_zero]
     add_smul := fun s₁ s₂ =>
       Localization.ind <|
-        Prod.rec <| by intros ; simp only [Localization.smul_mk, add_smul, add_mk_self] }
+        Prod.rec <| by intros; simp only [Localization.smul_mk, add_smul, add_mk_self] }
 
 instance {S : Type _} [CommSemiring S] [Algebra S R] : Algebra S (Localization M)
     where
@@ -1118,7 +1118,7 @@ protected irreducible_def neg (z : Localization M) : Localization M :=
   Localization.liftOn z (fun a b => mk (-a) b) fun a b c d h =>
     mk_eq_mk_iff.2
       (by
-        rw [r_eq_r'] at h⊢
+        rw [r_eq_r'] at h ⊢
         cases' h with t ht
         use t
         rw [mul_neg, mul_neg, ht]
@@ -1179,7 +1179,7 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
   rw [← (algebraMap R S).map_zero]
   constructor <;> intro h
   · cases' (eq_iff_exists M S).mp h with c hc
-    rw [MulZeroClass.mul_zero, mul_comm] at hc
+    rw [MulZeroClass.mul_zero, mul_comm] at hc 
     exact hM c.2 x hc
   · rw [h]
 #align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iff
@@ -1188,7 +1188,7 @@ protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraM
   by
   rw [injective_iff_map_eq_zero (algebraMap R S)]
   intro a ha
-  rwa [to_map_eq_zero_iff S hM] at ha
+  rwa [to_map_eq_zero_iff S hM] at ha 
 #align is_localization.injective IsLocalization.injective
 
 protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M ≤ nonZeroDivisors R)
@@ -1209,7 +1209,7 @@ theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDiv
   by
   have hsec := sec_spec M x
   intro hfst
-  rw [hfst, map_zero, mul_eq_zero, _root_.map_eq_zero_iff] at hsec
+  rw [hfst, map_zero, mul_eq_zero, _root_.map_eq_zero_iff] at hsec 
   · exact Or.elim hsec hx (sec_snd_ne_zero hM x)
   · exact IsLocalization.injective S hM
 #align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zero
@@ -1224,11 +1224,11 @@ theorem map_injective_of_injective (hg : Function.Injective g)
   rw [injective_iff_map_eq_zero]
   intro z hz
   obtain ⟨a, b, rfl⟩ := mk'_surjective M z
-  rw [map_mk', mk'_eq_zero_iff] at hz
+  rw [map_mk', mk'_eq_zero_iff] at hz 
   obtain ⟨⟨m', hm'⟩, hm⟩ := hz
-  rw [Submonoid.mem_map] at hm'
+  rw [Submonoid.mem_map] at hm' 
   obtain ⟨n, hn, hnm⟩ := hm'
-  rw [Subtype.coe_mk, ← hnm, ← map_mul, ← map_zero g] at hm
+  rw [Subtype.coe_mk, ← hnm, ← map_mul, ← map_zero g] at hm 
   rw [mk'_eq_zero_iff]
   exact ⟨⟨n, hn⟩, hg hm⟩
 #align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injective
@@ -1251,7 +1251,7 @@ theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [Is
       have :
         z * w * algebraMap A S y.2 * algebraMap A S x.2 = algebraMap A S x.1 * algebraMap A S y.1 :=
         by rw [mul_assoc z, hy, ← hx] <;> ring
-      rw [h, MulZeroClass.zero_mul, MulZeroClass.zero_mul, ← (algebraMap A S).map_mul] at this
+      rw [h, MulZeroClass.zero_mul, MulZeroClass.zero_mul, ← (algebraMap A S).map_mul] at this 
       cases' eq_zero_or_eq_zero_of_mul_eq_zero ((to_map_eq_zero_iff S hM).mp this.symm) with H H
       · exact Or.inl (eq_zero_of_fst_eq_zero hx H)
       · exact Or.inr (eq_zero_of_fst_eq_zero hy H) }

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

@@ -135,7 +135,7 @@ theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (al
         rintro ⟨c, hc⟩
         exact ⟨⟨c, h₁ c.2⟩, hc⟩
       · rintro ⟨c, h⟩
-        simpa only [[anonymous], map_mul, (h₂ c c.2).mul_right_inj] using
+        simpa only [SetLike.coe_mk, map_mul, (h₂ c c.2).mul_right_inj] using
           congr_arg (algebraMap R S) h }
 #align is_localization.of_le IsLocalization.of_le
 
@@ -466,7 +466,7 @@ theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (
   rw [mul_comm, ← one_mul z₁, ← Units.inv_mul (IsUnit.liftRight (g.to_monoid_hom.restrict M) h y),
     mul_assoc, ← mul_add, Units.inv_mul_eq_iff_eq_mul, Units.inv_mul_cancel_left,
     IsUnit.coe_liftRight]
-  simp only [RingHom.toMonoidHom_eq_coe, MonoidHom.restrict_apply, [anonymous]]
+  simp only [RingHom.toMonoidHom_eq_coe, MonoidHom.restrict_apply, RingHom.coe_monoidHom]
 #align is_localization.mul_add_inv_left IsLocalization.mul_add_inv_left
 
 theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w' v) :

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

@@ -92,7 +92,7 @@ commutative ring, field of fractions
 
 open Function
 
-open BigOperators
+open scoped BigOperators
 
 section CommSemiring
 

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

@@ -125,12 +125,6 @@ section
 
 variable (M)
 
-/- warning: is_localization.of_le -> IsLocalization.of_le is a dubious translation:
-lean 3 declaration is
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 theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (algebraMap R S r)) :
     IsLocalization N S :=
   { map_units := fun r => h₂ r r.2
@@ -167,20 +161,11 @@ abbrev toLocalizationMap : Submonoid.LocalizationMap M S :=
 #align is_localization.to_localization_map IsLocalization.toLocalizationMap
 -/
 
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 @[simp]
 theorem toLocalizationMap_toMap : (toLocalizationMap M S).toMap = (algebraMap R S : R →*₀ S) :=
   rfl
 #align is_localization.to_localization_map_to_map IsLocalization.toLocalizationMap_toMap
 
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 theorem toLocalizationMap_toMap_apply (x) : (toLocalizationMap M S).toMap x = algebraMap R S x :=
   rfl
 #align is_localization.to_localization_map_to_map_apply IsLocalization.toLocalizationMap_toMap_apply
@@ -189,32 +174,17 @@ end
 
 variable (M)
 
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 /-- Given a localization map `f : M →* N`, a section function sending `z : N` to some
 `(x, y) : M × S` such that `f x * (f y)⁻¹ = z`. -/
 noncomputable def sec (z : S) : R × M :=
   Classical.choose <| IsLocalization.surj _ z
 #align is_localization.sec IsLocalization.sec
 
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 @[simp]
 theorem toLocalizationMap_sec : (toLocalizationMap M S).sec = sec M :=
   rfl
 #align is_localization.to_localization_map_sec IsLocalization.toLocalizationMap_sec
 
-/- warning: is_localization.sec_spec -> IsLocalization.sec_spec is a dubious translation:
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 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x` (so this lemma is true by definition). -/
 theorem sec_spec (z : S) :
@@ -222,9 +192,6 @@ theorem sec_spec (z : S) :
   Classical.choose_spec <| IsLocalization.surj _ z
 #align is_localization.sec_spec IsLocalization.sec_spec
 
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 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x`, so this lemma is just an application of `S`'s commutativity. -/
 theorem sec_spec' (z : S) :
@@ -234,25 +201,16 @@ theorem sec_spec' (z : S) :
 
 variable {R M}
 
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 theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap R S (c * y)) :
     algebraMap R S x = algebraMap R S y :=
   (toLocalizationMap M S).map_right_cancel h
 #align is_localization.map_right_cancel IsLocalization.map_right_cancel
 
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 theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R S (y * c)) :
     algebraMap R S x = algebraMap R S y :=
   (toLocalizationMap M S).map_left_cancel h
 #align is_localization.map_left_cancel IsLocalization.map_left_cancel
 
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 theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebraMap R S x)
     (hx : x = 0) : z = 0 := by
   rw [hx, (algebraMap R S).map_zero] at h
@@ -261,9 +219,6 @@ theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebra
 
 variable (M S)
 
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 theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r = 0 :=
   by
   constructor
@@ -277,12 +232,6 @@ theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r =
 
 variable {M}
 
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 /-- `is_localization.mk' S` is the surjection sending `(x, y) : R × M` to
 `f x * (f y)⁻¹`. -/
 noncomputable def mk' (x : R) (y : M) : S :=
@@ -296,51 +245,30 @@ theorem mk'_sec (z : S) : mk' S (IsLocalization.sec M z).1 (IsLocalization.sec M
 #align is_localization.mk'_sec IsLocalization.mk'_sec
 -/
 
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 theorem mk'_mul (x₁ x₂ : R) (y₁ y₂ : M) : mk' S (x₁ * x₂) (y₁ * y₂) = mk' S x₁ y₁ * mk' S x₂ y₂ :=
   (toLocalizationMap M S).mk'_mul _ _ _ _
 #align is_localization.mk'_mul IsLocalization.mk'_mul
 
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 theorem mk'_one (x) : mk' S x (1 : M) = algebraMap R S x :=
   (toLocalizationMap M S).mk'_one _
 #align is_localization.mk'_one IsLocalization.mk'_one
 
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 @[simp]
 theorem mk'_spec (x) (y : M) : mk' S x y * algebraMap R S y = algebraMap R S x :=
   (toLocalizationMap M S).mk'_spec _ _
 #align is_localization.mk'_spec IsLocalization.mk'_spec
 
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 @[simp]
 theorem mk'_spec' (x) (y : M) : algebraMap R S y * mk' S x y = algebraMap R S x :=
   (toLocalizationMap M S).mk'_spec' _ _
 #align is_localization.mk'_spec' IsLocalization.mk'_spec'
 
-/- warning: is_localization.mk'_spec_mk -> IsLocalization.mk'_spec_mk is a dubious translation:
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 @[simp]
 theorem mk'_spec_mk (x) (y : R) (hy : y ∈ M) :
     mk' S x ⟨y, hy⟩ * algebraMap R S y = algebraMap R S x :=
   mk'_spec S x ⟨y, hy⟩
 #align is_localization.mk'_spec_mk IsLocalization.mk'_spec_mk
 
-/- warning: is_localization.mk'_spec'_mk -> IsLocalization.mk'_spec'_mk is a dubious translation:
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 @[simp]
 theorem mk'_spec'_mk (x) (y : R) (hy : y ∈ M) :
     algebraMap R S y * mk' S x ⟨y, hy⟩ = algebraMap R S x :=
@@ -349,25 +277,16 @@ theorem mk'_spec'_mk (x) (y : R) (hy : y ∈ M) :
 
 variable {S}
 
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 theorem eq_mk'_iff_mul_eq {x} {y : M} {z} :
     z = mk' S x y ↔ z * algebraMap R S y = algebraMap R S x :=
   (toLocalizationMap M S).eq_mk'_iff_mul_eq
 #align is_localization.eq_mk'_iff_mul_eq IsLocalization.eq_mk'_iff_mul_eq
 
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 theorem mk'_eq_iff_eq_mul {x} {y : M} {z} :
     mk' S x y = z ↔ algebraMap R S x = z * algebraMap R S y :=
   (toLocalizationMap M S).mk'_eq_iff_eq_mul
 #align is_localization.mk'_eq_iff_eq_mul IsLocalization.mk'_eq_iff_eq_mul
 
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 theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
     mk' S x y + z₁ = z₂ ↔ algebraMap R S x + z₁ * algebraMap R S y = z₂ * algebraMap R S y := by
   rw [← mk'_spec S x y, ← IsUnit.mul_left_inj (IsLocalization.map_units S y), right_distrib]
@@ -375,12 +294,6 @@ theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
 
 variable (M)
 
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 theorem mk'_surjective (z : S) : ∃ (x : _)(y : M), mk' S x y = z :=
   let ⟨r, hr⟩ := IsLocalization.surj _ z
   ⟨r.1, r.2, (eq_mk'_iff_mul_eq.2 hr).symm⟩
@@ -403,39 +316,21 @@ omit M
 
 variable {M S}
 
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 /-- Localizing at a submonoid with 0 inside it leads to the trivial ring. -/
 def uniqueOfZeroMem (h : (0 : R) ∈ M) : Unique S :=
   uniqueOfZeroEqOne <| by simpa using IsLocalization.map_units S ⟨0, h⟩
 #align is_localization.unique_of_zero_mem IsLocalization.uniqueOfZeroMem
 
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 theorem mk'_eq_iff_eq {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (y₂ * x₁) = algebraMap R S (y₁ * x₂) :=
   (toLocalizationMap M S).mk'_eq_iff_eq
 #align is_localization.mk'_eq_iff_eq IsLocalization.mk'_eq_iff_eq
 
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 theorem mk'_eq_iff_eq' {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (x₁ * y₂) = algebraMap R S (x₂ * y₁) :=
   (toLocalizationMap M S).mk'_eq_iff_eq'
 #align is_localization.mk'_eq_iff_eq' IsLocalization.mk'_eq_iff_eq'
 
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 theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R S x ∈ I :=
   by
   constructor <;> intro h
@@ -447,38 +342,20 @@ theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R
     rwa [mul_comm, mul_assoc, hb, mul_one] at this
 #align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iff
 
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 protected theorem eq {a₁ b₁} {a₂ b₂ : M} :
     mk' S a₁ a₂ = mk' S b₁ b₂ ↔ ∃ c : M, ↑c * (↑b₂ * a₁) = c * (a₂ * b₁) :=
   (toLocalizationMap M S).Eq
 #align is_localization.eq IsLocalization.eq
 
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 theorem mk'_eq_zero_iff (x : R) (s : M) : mk' S x s = 0 ↔ ∃ m : M, ↑m * x = 0 := by
   rw [← (map_units S s).mul_left_inj, mk'_spec, MulZeroClass.zero_mul, map_eq_zero_iff M]
 #align is_localization.mk'_eq_zero_iff IsLocalization.mk'_eq_zero_iff
 
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 @[simp]
 theorem mk'_zero (s : M) : IsLocalization.mk' S 0 s = 0 := by
   rw [eq_comm, IsLocalization.eq_mk'_iff_mul_eq, MulZeroClass.zero_mul, map_zero]
 #align is_localization.mk'_zero IsLocalization.mk'_zero
 
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 theorem ne_zero_of_mk'_ne_zero {x : R} {y : M} (hxy : IsLocalization.mk' S x y ≠ 0) : x ≠ 0 :=
   by
   rintro rfl
@@ -489,36 +366,21 @@ section Ext
 
 variable [Algebra R P] [IsLocalization M P]
 
-/- warning: is_localization.eq_iff_eq -> IsLocalization.eq_iff_eq is a dubious translation:
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 theorem eq_iff_eq {x y} :
     algebraMap R S x = algebraMap R S y ↔ algebraMap R P x = algebraMap R P y :=
   (toLocalizationMap M S).eq_iff_eq (toLocalizationMap M P)
 #align is_localization.eq_iff_eq IsLocalization.eq_iff_eq
 
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 theorem mk'_eq_iff_mk'_eq {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ mk' P x₁ y₁ = mk' P x₂ y₂ :=
   (toLocalizationMap M S).mk'_eq_iff_mk'_eq (toLocalizationMap M P)
 #align is_localization.mk'_eq_iff_mk'_eq IsLocalization.mk'_eq_iff_mk'_eq
 
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 theorem mk'_eq_of_eq {a₁ b₁ : R} {a₂ b₂ : M} (H : ↑a₂ * b₁ = ↑b₂ * a₁) :
     mk' S a₁ a₂ = mk' S b₁ b₂ :=
   (toLocalizationMap M S).mk'_eq_of_eq H
 #align is_localization.mk'_eq_of_eq IsLocalization.mk'_eq_of_eq
 
-/- warning: is_localization.mk'_eq_of_eq' -> IsLocalization.mk'_eq_of_eq' is a dubious translation:
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 theorem mk'_eq_of_eq' {a₁ b₁ : R} {a₂ b₂ : M} (H : b₁ * ↑a₂ = a₁ * ↑b₂) :
     mk' S a₁ a₂ = mk' S b₁ b₂ :=
   (toLocalizationMap M S).mk'_eq_of_eq' H
@@ -526,84 +388,45 @@ theorem mk'_eq_of_eq' {a₁ b₁ : R} {a₂ b₂ : M} (H : b₁ * ↑a₂ = a₁
 
 variable (S)
 
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 @[simp]
 theorem mk'_self {x : R} (hx : x ∈ M) : mk' S x ⟨x, hx⟩ = 1 :=
   (toLocalizationMap M S).mk'_self _ hx
 #align is_localization.mk'_self IsLocalization.mk'_self
 
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 @[simp]
 theorem mk'_self' {x : M} : mk' S (x : R) x = 1 :=
   (toLocalizationMap M S).mk'_self' _
 #align is_localization.mk'_self' IsLocalization.mk'_self'
 
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 theorem mk'_self'' {x : M} : mk' S x.1 x = 1 :=
   mk'_self' _
 #align is_localization.mk'_self'' IsLocalization.mk'_self''
 
 end Ext
 
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 theorem mul_mk'_eq_mk'_of_mul (x y : R) (z : M) :
     (algebraMap R S) x * mk' S y z = mk' S (x * y) z :=
   (toLocalizationMap M S).mul_mk'_eq_mk'_of_mul _ _ _
 #align is_localization.mul_mk'_eq_mk'_of_mul IsLocalization.mul_mk'_eq_mk'_of_mul
 
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-Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_mul_mk'_one IsLocalization.mk'_eq_mul_mk'_oneₓ'. -/
 theorem mk'_eq_mul_mk'_one (x : R) (y : M) : mk' S x y = (algebraMap R S) x * mk' S 1 y :=
   ((toLocalizationMap M S).mul_mk'_one_eq_mk' _ _).symm
 #align is_localization.mk'_eq_mul_mk'_one IsLocalization.mk'_eq_mul_mk'_one
 
-/- warning: is_localization.mk'_mul_cancel_left -> IsLocalization.mk'_mul_cancel_left is a dubious translation:
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 @[simp]
 theorem mk'_mul_cancel_left (x : R) (y : M) : mk' S (y * x : R) y = (algebraMap R S) x :=
   (toLocalizationMap M S).mk'_mul_cancel_left _ _
 #align is_localization.mk'_mul_cancel_left IsLocalization.mk'_mul_cancel_left
 
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 theorem mk'_mul_cancel_right (x : R) (y : M) : mk' S (x * y) y = (algebraMap R S) x :=
   (toLocalizationMap M S).mk'_mul_cancel_right _ _
 #align is_localization.mk'_mul_cancel_right IsLocalization.mk'_mul_cancel_right
 
-/- warning: is_localization.mk'_mul_mk'_eq_one -> IsLocalization.mk'_mul_mk'_eq_one is a dubious translation:
-<too large>
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 @[simp]
 theorem mk'_mul_mk'_eq_one (x y : M) : mk' S (x : R) y * mk' S (y : R) x = 1 := by
   rw [← mk'_mul, mul_comm] <;> exact mk'_self _ _
 #align is_localization.mk'_mul_mk'_eq_one IsLocalization.mk'_mul_mk'_eq_one
 
-/- warning: is_localization.mk'_mul_mk'_eq_one' -> IsLocalization.mk'_mul_mk'_eq_one' is a dubious translation:
-<too large>
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 theorem mk'_mul_mk'_eq_one' (x : R) (y : M) (h : x ∈ M) : mk' S x y * mk' S (y : R) ⟨x, h⟩ = 1 :=
   mk'_mul_mk'_eq_one ⟨x, h⟩ _
 #align is_localization.mk'_mul_mk'_eq_one' IsLocalization.mk'_mul_mk'_eq_one'
@@ -612,18 +435,12 @@ section
 
 variable (M)
 
-/- warning: is_localization.is_unit_comp -> IsLocalization.isUnit_comp is a dubious translation:
-<too large>
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 theorem isUnit_comp (j : S →+* P) (y : M) : IsUnit (j.comp (algebraMap R S) y) :=
   (toLocalizationMap M S).isUnit_comp j.toMonoidHom _
 #align is_localization.is_unit_comp IsLocalization.isUnit_comp
 
 end
 
-/- warning: is_localization.eq_of_eq -> IsLocalization.eq_of_eq is a dubious translation:
-<too large>
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 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g(M) ⊆ units P`, `f x = f y → g x = g y` for all `x y : R`. -/
 theorem eq_of_eq {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) {x y}
@@ -631,9 +448,6 @@ theorem eq_of_eq {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) {x y}
   @Submonoid.LocalizationMap.eq_of_eq _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom hg _ _ h
 #align is_localization.eq_of_eq IsLocalization.eq_of_eq
 
-/- warning: is_localization.mk'_add -> IsLocalization.mk'_add is a dubious translation:
-<too large>
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 theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
     mk' S (x₁ * y₂ + x₂ * y₁) (y₁ * y₂) = mk' S x₁ y₁ + mk' S x₂ y₂ :=
   mk'_eq_iff_eq_mul.2 <|
@@ -646,9 +460,6 @@ theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
         ring)
 #align is_localization.mk'_add IsLocalization.mk'_add
 
-/- warning: is_localization.mul_add_inv_left -> IsLocalization.mul_add_inv_left is a dubious translation:
-<too large>
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 theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (w z₁ z₂ : P) :
     w * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) h y)⁻¹ + z₁ = z₂ ↔ w + g y * z₁ = g y * z₂ :=
   by
@@ -658,9 +469,6 @@ theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (
   simp only [RingHom.toMonoidHom_eq_coe, MonoidHom.restrict_apply, [anonymous]]
 #align is_localization.mul_add_inv_left IsLocalization.mul_add_inv_left
 
-/- warning: is_localization.lift_spec_mul_add -> IsLocalization.lift_spec_mul_add is a dubious translation:
-<too large>
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 theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w' v) :
     ((toLocalizationWithZeroMap M S).lift g.toMonoidWithZeroHom hg) z * w + w' = v ↔
       g ((toLocalizationMap M S).sec z).1 * w + g ((toLocalizationMap M S).sec z).2 * w' =
@@ -671,9 +479,6 @@ theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w'
   rfl
 #align is_localization.lift_spec_mul_add IsLocalization.lift_spec_mul_add
 
-/- warning: is_localization.lift -> IsLocalization.lift is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.lift IsLocalization.liftₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
 `S` to `P` sending `z : S` to `g x * (g y)⁻¹`, where `(x, y) : R × M` are such that
@@ -696,9 +501,6 @@ noncomputable def lift {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) : S →+*
 
 variable {g : R →+* P} (hg : ∀ y : M, IsUnit (g y))
 
-/- warning: is_localization.lift_mk' -> IsLocalization.lift_mk' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk' IsLocalization.lift_mk'ₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
 `S` to `P` maps `f x * (f y)⁻¹` to `g x * (g y)⁻¹` for all `x : R, y ∈ M`. -/
@@ -707,43 +509,25 @@ theorem lift_mk' (x y) :
   (toLocalizationMap M S).lift_mk' _ _ _
 #align is_localization.lift_mk' IsLocalization.lift_mk'
 
-/- warning: is_localization.lift_mk'_spec -> IsLocalization.lift_mk'_spec is a dubious translation:
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 theorem lift_mk'_spec (x v) (y : M) : lift hg (mk' S x y) = v ↔ g x = g y * v :=
   (toLocalizationMap M S).lift_mk'_spec _ _ _ _
 #align is_localization.lift_mk'_spec IsLocalization.lift_mk'_spec
 
-/- warning: is_localization.lift_eq -> IsLocalization.lift_eq is a dubious translation:
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 @[simp]
 theorem lift_eq (x : R) : lift hg ((algebraMap R S) x) = g x :=
   (toLocalizationMap M S).liftEq _ _
 #align is_localization.lift_eq IsLocalization.lift_eq
 
-/- warning: is_localization.lift_eq_iff -> IsLocalization.lift_eq_iff is a dubious translation:
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 theorem lift_eq_iff {x y : R × M} :
     lift hg (mk' S x.1 x.2) = lift hg (mk' S y.1 y.2) ↔ g (x.1 * y.2) = g (y.1 * x.2) :=
   (toLocalizationMap M S).lift_eq_iff _
 #align is_localization.lift_eq_iff IsLocalization.lift_eq_iff
 
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 @[simp]
 theorem lift_comp : (lift hg).comp (algebraMap R S) = g :=
   RingHom.ext <| MonoidHom.ext_iff.1 <| (toLocalizationMap M S).lift_comp _
 #align is_localization.lift_comp IsLocalization.lift_comp
 
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 @[simp]
 theorem lift_of_comp (j : S →+* P) : lift (isUnit_comp M j) = j :=
   RingHom.ext <| MonoidHom.ext_iff.1 <| (toLocalizationMap M S).lift_of_comp j.toMonoidHom
@@ -751,33 +535,18 @@ theorem lift_of_comp (j : S →+* P) : lift (isUnit_comp M j) = j :=
 
 variable (M)
 
-/- warning: is_localization.monoid_hom_ext -> IsLocalization.monoidHom_ext is a dubious translation:
-<too large>
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 /-- See note [partially-applied ext lemmas] -/
 theorem monoidHom_ext ⦃j k : S →* P⦄
     (h : j.comp (algebraMap R S : R →* S) = k.comp (algebraMap R S)) : j = k :=
   Submonoid.LocalizationMap.epic_of_localizationMap (toLocalizationMap M S) <| MonoidHom.congr_fun h
 #align is_localization.monoid_hom_ext IsLocalization.monoidHom_ext
 
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 /-- See note [partially-applied ext lemmas] -/
 theorem ringHom_ext ⦃j k : S →+* P⦄ (h : j.comp (algebraMap R S) = k.comp (algebraMap R S)) :
     j = k :=
   RingHom.coe_monoidHom_injective <| monoidHom_ext M <| MonoidHom.ext <| RingHom.congr_fun h
 #align is_localization.ring_hom_ext IsLocalization.ringHom_ext
 
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 /- This is not an instance because the submonoid `M` would become a metavariable
   in typeclass search. -/
 theorem algHom_subsingleton [Algebra R P] : Subsingleton (S →ₐ[R] P) :=
@@ -786,9 +555,6 @@ theorem algHom_subsingleton [Algebra R P] : Subsingleton (S →ₐ[R] P) :=
       IsLocalization.ringHom_ext M <| by rw [f.comp_algebra_map, g.comp_algebra_map]⟩
 #align is_localization.alg_hom_subsingleton IsLocalization.algHom_subsingleton
 
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 /-- To show `j` and `k` agree on the whole localization, it suffices to show they agree
 on the image of the base ring, if they preserve `1` and `*`. -/
 protected theorem ext (j k : S → P) (hj1 : j 1 = 1) (hk1 : k 1 = 1)
@@ -799,9 +565,6 @@ protected theorem ext (j k : S → P) (hj1 : j 1 = 1) (hk1 : k 1 = 1)
 
 variable {M}
 
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 theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) : lift hg = j :=
   RingHom.ext <|
     MonoidHom.ext_iff.1 <|
@@ -809,28 +572,16 @@ theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) :
         j.toMonoidHom hj
 #align is_localization.lift_unique IsLocalization.lift_unique
 
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 @[simp]
 theorem lift_id (x) : lift (map_units S : ∀ y : M, IsUnit _) x = x :=
   (toLocalizationMap M S).lift_id _
 #align is_localization.lift_id IsLocalization.lift_id
 
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 theorem lift_surjective_iff :
     Surjective (lift hg : S → P) ↔ ∀ v : P, ∃ x : R × M, v * g x.2 = g x.1 :=
   (toLocalizationMap M S).lift_surjective_iff hg
 #align is_localization.lift_surjective_iff IsLocalization.lift_surjective_iff
 
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 theorem lift_injective_iff :
     Injective (lift hg : S → P) ↔ ∀ x y, algebraMap R S x = algebraMap R S y ↔ g x = g y :=
   (toLocalizationMap M S).lift_injective_iff hg
@@ -846,9 +597,6 @@ section
 
 variable (Q)
 
-/- warning: is_localization.map -> IsLocalization.map is a dubious translation:
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 /-- Map a homomorphism `g : R →+* P` to `S →+* Q`, where `S` and `Q` are
 localizations of `R` and `P` at `M` and `T` respectively,
 such that `g(M) ⊆ T`.
@@ -861,49 +609,31 @@ noncomputable def map (g : R →+* P) (hy : M ≤ T.comap g) : S →+* Q :=
 
 end
 
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 theorem map_eq (x) : map Q g hy ((algebraMap R S) x) = algebraMap P Q (g x) :=
   lift_eq (fun y => map_units _ ⟨g y, hy y.2⟩) x
 #align is_localization.map_eq IsLocalization.map_eq
 
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 @[simp]
 theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g :=
   lift_comp fun y => map_units _ ⟨g y, hy y.2⟩
 #align is_localization.map_comp IsLocalization.map_comp
 
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 theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.2⟩ :=
   @Submonoid.LocalizationMap.map_mk' _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom _
     (fun y => hy y.2) _ _ (toLocalizationMap T Q) _ _
 #align is_localization.map_mk' IsLocalization.map_mk'
 
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 @[simp]
 theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
     map S (RingHom.id _) h z = z :=
   lift_id _
 #align is_localization.map_id IsLocalization.map_id
 
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-<too large>
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 theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algebraMap P Q (g x)) :
     map Q g hy = j :=
   lift_unique (fun y => map_units _ ⟨g y, hy y.2⟩) hj
 #align is_localization.map_unique IsLocalization.map_unique
 
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-<too large>
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 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
 theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W]
@@ -914,9 +644,6 @@ theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSe
       (toLocalizationMap U W) l _ x
 #align is_localization.map_comp_map IsLocalization.map_comp_map
 
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-<too large>
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 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
 theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W] [Algebra A W]
@@ -925,9 +652,6 @@ theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemirin
   rw [← map_comp_map hy hl] <;> rfl
 #align is_localization.map_map IsLocalization.map_map
 
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-<too large>
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 theorem map_smul (x : S) (z : R) : map Q g hy (z • x : S) = g z • map Q g hy x := by
   rw [Algebra.smul_def, Algebra.smul_def, RingHom.map_mul, map_eq]
 #align is_localization.map_smul IsLocalization.map_smul
@@ -936,12 +660,6 @@ section
 
 variable (S Q)
 
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-Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv IsLocalization.ringEquivOfRingEquivₓ'. -/
 /-- If `S`, `Q` are localizations of `R` and `P` at submonoids `M, T` respectively, an
 isomorphism `j : R ≃+* P` such that `j(M) = T` induces an isomorphism of localizations
 `S ≃+* Q`. -/
@@ -966,27 +684,18 @@ noncomputable def ringEquivOfRingEquiv (h : R ≃+* P) (H : M.map h.toMonoidHom
 
 end
 
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-<too large>
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 theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T) :
     (ringEquivOfRingEquiv S Q j H : S →+* Q) =
       map Q (j : R →+* P) (M.le_comap_of_map_le (le_of_eq H)) :=
   rfl
 #align is_localization.ring_equiv_of_ring_equiv_eq_map IsLocalization.ringEquivOfRingEquiv_eq_map
 
-/- warning: is_localization.ring_equiv_of_ring_equiv_eq -> IsLocalization.ringEquivOfRingEquiv_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eqₓ'. -/
 @[simp]
 theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x) :
     ringEquivOfRingEquiv S Q j H ((algebraMap R S) x) = algebraMap P Q (j x) :=
   map_eq _ _
 #align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eq
 
-/- warning: is_localization.ring_equiv_of_ring_equiv_mk' -> IsLocalization.ringEquivOfRingEquiv_mk' is a dubious translation:
-<too large>
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 theorem ringEquivOfRingEquiv_mk' {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x : R) (y : M) :
     ringEquivOfRingEquiv S Q j H (mk' S x y) =
       mk' Q (j x) ⟨j y, show j y ∈ T from H ▸ Set.mem_image_of_mem j y.2⟩ :=
@@ -1015,17 +724,11 @@ noncomputable def algEquiv : S ≃ₐ[R] Q :=
 
 end
 
-/- warning: is_localization.alg_equiv_mk' -> IsLocalization.algEquiv_mk' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
   map_mk' _ _ _
 #align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'
 
-/- warning: is_localization.alg_equiv_symm_mk' -> IsLocalization.algEquiv_symm_mk' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.alg_equiv_symm_mk' IsLocalization.algEquiv_symm_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) = mk' S x y :=
   map_mk' _ _ _
@@ -1039,12 +742,6 @@ section
 
 variable (M)
 
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 theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃ₐ[R] P) :
     IsLocalization M P := by
   constructor
@@ -1062,23 +759,11 @@ theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃
     rfl
 #align is_localization.is_localization_of_alg_equiv IsLocalization.isLocalization_of_algEquiv
 
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 theorem isLocalization_iff_of_algEquiv [Algebra R P] (h : S ≃ₐ[R] P) :
     IsLocalization M S ↔ IsLocalization M P :=
   ⟨fun _ => is_localization_of_alg_equiv M h, fun _ => is_localization_of_alg_equiv M h.symm⟩
 #align is_localization.is_localization_iff_of_alg_equiv IsLocalization.isLocalization_iff_of_algEquiv
 
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-Case conversion may be inaccurate. Consider using '#align is_localization.is_localization_iff_of_ring_equiv IsLocalization.isLocalization_iff_of_ringEquivₓ'. -/
 theorem isLocalization_iff_of_ringEquiv (h : S ≃+* P) :
     IsLocalization M S ↔ @IsLocalization _ M P _ (h.toRingHom.comp <| algebraMap R S).toAlgebra :=
   letI := (h.to_ring_hom.comp <| algebraMap R S).toAlgebra
@@ -1087,12 +772,6 @@ theorem isLocalization_iff_of_ringEquiv (h : S ≃+* P) :
 
 variable (S)
 
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-Case conversion may be inaccurate. Consider using '#align is_localization.is_localization_of_base_ring_equiv IsLocalization.isLocalization_of_base_ringEquivₓ'. -/
 theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
     @IsLocalization _ (M.map h.toMonoidHom) S _
       ((algebraMap R S).comp h.symm.toRingHom).toAlgebra :=
@@ -1117,12 +796,6 @@ theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
       ⟨fun ⟨c, e⟩ => ⟨⟨_, _, c.Prop, rfl⟩, e⟩, fun ⟨⟨_, c, h, e₁⟩, e₂⟩ => ⟨⟨_, h⟩, e₁.symm ▸ e₂⟩⟩
 #align is_localization.is_localization_of_base_ring_equiv IsLocalization.isLocalization_of_base_ringEquiv
 
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-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] (h : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))), Iff (IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3) (IsLocalization.{u3, u2} P _inst_4 (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) h) M) S _inst_2 (RingHom.toAlgebra.{u3, u2} P S _inst_4 _inst_2 (RingHom.comp.{u3, u1, u2} P R S (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (RingEquiv.toRingHom.{u3, u1} P R (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingEquiv.symm.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) h)))))
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-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] (h : RingEquiv.{u3, u2} R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Distrib.toAdd.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Distrib.toAdd.{u2} P (NonUnitalNonAssocSemiring.toDistrib.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))), Iff (IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3) (IsLocalization.{u2, u1} P _inst_4 (Submonoid.map.{u3, u2, max u3 u2} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MonoidHom.{u3, u2} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (MonoidHom.monoidHomClass.{u3, u2} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (RingEquiv.toMonoidHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) h) M) S _inst_2 (RingHom.toAlgebra.{u2, u1} P S _inst_4 _inst_2 (RingHom.comp.{u2, u3, u1} P R S (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (algebraMap.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (RingEquiv.toRingHom.{u2, u3} P R (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingEquiv.symm.{u3, u2} R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Distrib.toAdd.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Distrib.toAdd.{u2} P (NonUnitalNonAssocSemiring.toDistrib.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) h)))))
-Case conversion may be inaccurate. Consider using '#align is_localization.is_localization_iff_of_base_ring_equiv IsLocalization.isLocalization_iff_of_base_ringEquivₓ'. -/
 theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
     IsLocalization M S ↔
       @IsLocalization _ (M.map h.toMonoidHom) S _
@@ -1147,12 +820,6 @@ variable (M S)
 
 include M
 
-/- warning: is_localization.non_zero_divisors_le_comap -> IsLocalization.nonZeroDivisors_le_comap is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3], LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (nonZeroDivisors.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))
-Case conversion may be inaccurate. Consider using '#align is_localization.non_zero_divisors_le_comap IsLocalization.nonZeroDivisors_le_comapₓ'. -/
 theorem nonZeroDivisors_le_comap [IsLocalization M S] :
     nonZeroDivisors R ≤ (nonZeroDivisors S).comap (algebraMap R S) :=
   by
@@ -1166,12 +833,6 @@ theorem nonZeroDivisors_le_comap [IsLocalization M S] :
   exact ⟨c, ha _ e⟩
 #align is_localization.non_zero_divisors_le_comap IsLocalization.nonZeroDivisors_le_comap
 
-/- warning: is_localization.map_non_zero_divisors_le -> IsLocalization.map_nonZeroDivisors_le is a dubious translation:
-lean 3 declaration is
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 theorem map_nonZeroDivisors_le [IsLocalization M S] :
     (nonZeroDivisors R).map (algebraMap R S) ≤ nonZeroDivisors S :=
   Submonoid.map_le_iff_le_comap.mpr (nonZeroDivisors_le_comap M S)
@@ -1221,19 +882,10 @@ protected irreducible_def add (z w : Localization M) : Localization M :=
 instance : Add (Localization M) :=
   ⟨Localization.add⟩
 
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 theorem add_mk (a b c d) : (mk a b : Localization M) + mk c d = mk (b * c + d * a) (b * d) := by
   unfold Add.add Localization.add; apply lift_on₂_mk
 #align localization.add_mk Localization.add_mk
 
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 theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b :=
   by
   rw [add_mk, mk_eq_mk_iff, r_eq_r']
@@ -1295,12 +947,6 @@ instance : CommSemiring (Localization M) :=
           run_tac
             tac) }
 
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 /-- For any given denominator `b : M`, the map `a ↦ a / b` is an `add_monoid_hom` from `R` to
   `localization M`-/
 @[simps]
@@ -1311,33 +957,15 @@ def mkAddMonoidHom (b : M) : R →+ Localization M
   map_add' x y := (add_mk_self _ _ _).symm
 #align localization.mk_add_monoid_hom Localization.mkAddMonoidHom
 
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 theorem mk_sum {ι : Type _} (f : ι → R) (s : Finset ι) (b : M) :
     mk (∑ i in s, f i) b = ∑ i in s, mk (f i) b :=
   (mkAddMonoidHom b).map_sum f s
 #align localization.mk_sum Localization.mk_sum
 
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 theorem mk_list_sum (l : List R) (b : M) : mk l.Sum b = (l.map fun a => mk a b).Sum :=
   (mkAddMonoidHom b).map_list_sum l
 #align localization.mk_list_sum Localization.mk_list_sum
 
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 theorem mk_multiset_sum (l : Multiset R) (b : M) : mk l.Sum b = (l.map fun a => mk a b).Sum :=
   (mkAddMonoidHom b).map_multiset_sum l
 #align localization.mk_multiset_sum Localization.mk_multiset_sum
@@ -1400,66 +1028,33 @@ instance : IsLocalization M (Localization M)
 
 end
 
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 @[simp]
 theorem toLocalizationMap_eq_monoidOf : toLocalizationMap M (Localization M) = monoidOf M :=
   rfl
 #align localization.to_localization_map_eq_monoid_of Localization.toLocalizationMap_eq_monoidOf
 
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 theorem monoidOf_eq_algebraMap (x) : (monoidOf M).toMap x = algebraMap R (Localization M) x :=
   rfl
 #align localization.monoid_of_eq_algebra_map Localization.monoidOf_eq_algebraMap
 
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 theorem mk_one_eq_algebraMap (x) : mk x 1 = algebraMap R (Localization M) x :=
   rfl
 #align localization.mk_one_eq_algebra_map Localization.mk_one_eq_algebraMap
 
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 theorem mk_eq_mk'_apply (x y) : mk x y = IsLocalization.mk' (Localization M) x y := by
   rw [mk_eq_monoid_of_mk'_apply, mk', to_localization_map_eq_monoid_of]
 #align localization.mk_eq_mk'_apply Localization.mk_eq_mk'_apply
 
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 @[simp]
 theorem mk_eq_mk' : (mk : R → M → Localization M) = IsLocalization.mk' (Localization M) :=
   mk_eq_monoidOf_mk'
 #align localization.mk_eq_mk' Localization.mk_eq_mk'
 
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 theorem mk_algebraMap {A : Type _} [CommSemiring A] [Algebra A R] (m : A) :
     mk (algebraMap A R m) 1 = algebraMap A (Localization M) m := by
   rw [mk_eq_mk', mk'_eq_iff_eq_mul, Submonoid.coe_one, map_one, mul_one] <;> rfl
 #align localization.mk_algebra_map Localization.mk_algebraMap
 
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 theorem mk_nat_cast (m : ℕ) : (mk m 1 : Localization M) = m := by
   simpa using @mk_algebra_map R _ M ℕ _ _ m
 #align localization.mk_nat_cast Localization.mk_nat_cast
@@ -1470,12 +1065,6 @@ section
 
 variable (M S)
 
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 /-- The localization of `R` at `M` as a quotient type is isomorphic to any other localization. -/
 @[simps]
 noncomputable def algEquiv : Localization M ≃ₐ[R] S :=
@@ -1493,32 +1082,20 @@ noncomputable def IsLocalization.unique (R Rₘ) [CommSemiring R] [CommSemiring
 
 end
 
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 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) = mk' S x y :=
   algEquiv_mk' _ _
 #align localization.alg_equiv_mk' Localization.algEquiv_mk'
 
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 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) :
     (algEquiv M S).symm (mk' S x y) = mk' (Localization M) x y :=
   algEquiv_symm_mk' _ _
 #align localization.alg_equiv_symm_mk' Localization.algEquiv_symm_mk'
 
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 theorem algEquiv_mk (x y) : algEquiv M S (mk x y) = mk' S x y := by rw [mk_eq_mk', alg_equiv_mk']
 #align localization.alg_equiv_mk Localization.algEquiv_mk
 
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 theorem algEquiv_symm_mk (x : R) (y : M) : (algEquiv M S).symm (mk' S x y) = mk x y := by
   rw [mk_eq_mk', alg_equiv_symm_mk']
 #align localization.alg_equiv_symm_mk Localization.algEquiv_symm_mk
@@ -1552,12 +1129,6 @@ protected irreducible_def neg (z : Localization M) : Localization M :=
 instance : Neg (Localization M) :=
   ⟨Localization.neg⟩
 
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 theorem neg_mk (a b) : -(mk a b : Localization M) = mk (-a) b := by unfold Neg.neg Localization.neg;
   apply lift_on_mk
 #align localization.neg_mk Localization.neg_mk
@@ -1584,9 +1155,6 @@ instance : CommRing (Localization M) :=
           simp only [Submonoid.coe_mul]
           ring) }
 
-/- warning: localization.sub_mk -> Localization.sub_mk is a dubious translation:
-<too large>
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 theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b * c) (b * d) :=
   calc
     mk a b - mk c d = mk a b + -mk c d := sub_eq_add_neg _ _
@@ -1596,12 +1164,6 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b
     
 #align localization.sub_mk Localization.sub_mk
 
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 theorem mk_int_cast (m : ℤ) : (mk m 1 : Localization M) = m := by
   simpa using @mk_algebra_map R _ M ℤ _ _ m
 #align localization.mk_int_cast Localization.mk_int_cast
@@ -1612,12 +1174,6 @@ namespace IsLocalization
 
 variable {R M} (S) {K : Type _} [IsLocalization M S]
 
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-Case conversion may be inaccurate. Consider using '#align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iffₓ'. -/
 theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R S x = 0 ↔ x = 0 :=
   by
   rw [← (algebraMap R S).map_zero]
@@ -1628,12 +1184,6 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
   · rw [h]
 #align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iff
 
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 protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraMap R S) :=
   by
   rw [injective_iff_map_eq_zero (algebraMap R S)]
@@ -1641,9 +1191,6 @@ protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraM
   rwa [to_map_eq_zero_iff S hM] at ha
 #align is_localization.injective IsLocalization.injective
 
-/- warning: is_localization.to_map_ne_zero_of_mem_non_zero_divisors -> IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisors is a dubious translation:
-<too large>
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 protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M ≤ nonZeroDivisors R)
     {x : R} (hx : x ∈ nonZeroDivisors R) : algebraMap R S x ≠ 0 :=
   show (algebraMap R S).toMonoidWithZeroHom x ≠ 0 from
@@ -1652,17 +1199,11 @@ protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M 
 
 variable {S}
 
-/- warning: is_localization.sec_snd_ne_zero -> IsLocalization.sec_snd_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.sec_snd_ne_zero IsLocalization.sec_snd_ne_zeroₓ'. -/
 theorem sec_snd_ne_zero [Nontrivial R] (hM : M ≤ nonZeroDivisors R) (x : S) :
     ((sec M x).snd : R) ≠ 0 :=
   nonZeroDivisors.coe_ne_zero ⟨(sec M x).snd.val, hM (sec M x).snd.property⟩
 #align is_localization.sec_snd_ne_zero IsLocalization.sec_snd_ne_zero
 
-/- warning: is_localization.sec_fst_ne_zero -> IsLocalization.sec_fst_ne_zero is a dubious translation:
-<too large>
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 theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDivisors R) {x : S}
     (hx : x ≠ 0) : (sec M x).fst ≠ 0 :=
   by
@@ -1675,9 +1216,6 @@ theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDiv
 
 variable (S M) (Q : Type _) [CommRing Q] {g : R →+* P} [Algebra P Q]
 
-/- warning: is_localization.map_injective_of_injective -> IsLocalization.map_injective_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injectiveₓ'. -/
 /-- Injectivity of a map descends to the map induced on localizations. -/
 theorem map_injective_of_injective (hg : Function.Injective g)
     [IsLocalization (M.map g : Submonoid P) Q] :
@@ -1699,12 +1237,6 @@ variable {S Q M}
 
 variable (A : Type _) [CommRing A] [IsDomain A]
 
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-Case conversion may be inaccurate. Consider using '#align is_localization.no_zero_divisors_of_le_non_zero_divisors IsLocalization.noZeroDivisors_of_le_nonZeroDivisorsₓ'. -/
 /-- A `comm_ring` `S` which is the localization of a ring `R` without zero divisors at a subset of
 non-zero elements does not have zero divisors.
 See note [reducible non-instances]. -/
@@ -1725,12 +1257,6 @@ theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [Is
       · exact Or.inr (eq_zero_of_fst_eq_zero hy H) }
 #align is_localization.no_zero_divisors_of_le_non_zero_divisors IsLocalization.noZeroDivisors_of_le_nonZeroDivisors
 
-/- warning: is_localization.is_domain_of_le_non_zero_divisors -> IsLocalization.isDomain_of_le_nonZeroDivisors is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_localization.is_domain_of_le_non_zero_divisors IsLocalization.isDomain_of_le_nonZeroDivisorsₓ'. -/
 /-- A `comm_ring` `S` which is the localization of an integral domain `R` at a subset of
 non-zero elements is an integral domain.
 See note [reducible non-instances]. -/
@@ -1748,12 +1274,6 @@ theorem isDomain_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [IsLocali
 
 variable {A}
 
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 /-- The localization at of an integral domain to a set of non-zero elements is an integral domain.
 See note [reducible non-instances]. -/
 @[reducible]
@@ -1766,12 +1286,6 @@ end IsLocalization
 
 open IsLocalization
 
-/- warning: is_field.localization_map_bijective -> IsField.localization_map_bijective is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_field.localization_map_bijective IsField.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommRing Rₘ]
     {M : Submonoid R} (hM : (0 : R) ∉ M) (hR : IsField R) [Algebra R Rₘ] [IsLocalization M Rₘ] :
@@ -1785,12 +1299,6 @@ theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommR
   exact ⟨r * n, by erw [eq_mk'_iff_mul_eq, ← map_mul, mul_assoc, mul_comm n, hn, mul_one]⟩
 #align is_field.localization_map_bijective IsField.localization_map_bijective
 
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-Case conversion may be inaccurate. Consider using '#align field.localization_map_bijective Field.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem Field.localization_map_bijective {K Kₘ : Type _} [Field K] [CommRing Kₘ] {M : Submonoid K}
     (hM : (0 : K) ∉ M) [Algebra K Kₘ] [IsLocalization M Kₘ] :
@@ -1840,18 +1348,12 @@ variable (S Rₘ Sₘ)
 
 include S
 
-/- warning: is_localization.map_units_map_submonoid -> IsLocalization.map_units_map_submonoid is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoidₓ'. -/
 theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R Sₘ y) :=
   by
   rw [IsScalarTower.algebraMap_apply _ S]
   exact IsLocalization.map_units Sₘ ⟨algebraMap R S y, Algebra.mem_algebraMapSubmonoid_of_mem y⟩
 #align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoid
 
-/- warning: is_localization.algebra_map_mk' -> IsLocalization.algebraMap_mk' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_mk' IsLocalization.algebraMap_mk'ₓ'. -/
 @[simp]
 theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
     algebraMap Rₘ Sₘ (IsLocalization.mk' Rₘ x y) =
@@ -1867,9 +1369,6 @@ theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
 
 variable (M)
 
-/- warning: is_localization.algebra_map_eq_map_map_submonoid -> IsLocalization.algebraMap_eq_map_map_submonoid is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_eq_map_map_submonoid IsLocalization.algebraMap_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
 R  →  S
@@ -1886,9 +1385,6 @@ theorem IsLocalization.algebraMap_eq_map_map_submonoid :
       rw [← IsScalarTower.algebraMap_apply R S Sₘ, ← IsScalarTower.algebraMap_apply R Rₘ Sₘ]
 #align is_localization.algebra_map_eq_map_map_submonoid IsLocalization.algebraMap_eq_map_map_submonoid
 
-/- warning: is_localization.algebra_map_apply_eq_map_map_submonoid -> IsLocalization.algebraMap_apply_eq_map_map_submonoid is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
 R  →  S
@@ -1905,9 +1401,6 @@ theorem IsLocalization.algebraMap_apply_eq_map_map_submonoid (x) :
 
 variable {R}
 
-/- warning: is_localization.lift_algebra_map_eq_algebra_map -> IsLocalization.lift_algebraMap_eq_algebraMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.lift_algebra_map_eq_algebra_map IsLocalization.lift_algebraMap_eq_algebraMapₓ'. -/
 theorem IsLocalization.lift_algebraMap_eq_algebraMap :
     @IsLocalization.lift R _ M Rₘ _ _ Sₘ _ _ (algebraMap R Sₘ)
         (IsLocalization.map_units_map_submonoid S Sₘ) =
@@ -1919,9 +1412,6 @@ end
 
 variable (Rₘ Sₘ)
 
-/- warning: localization_algebra_injective -> localizationAlgebra_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localization_algebra_injective localizationAlgebra_injectiveₓ'. -/
 /-- Injectivity of the underlying `algebra_map` descends to the algebra induced by localization. -/
 theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)) :
     Function.Injective (@algebraMap Rₘ Sₘ _ _ (localizationAlgebra M S)) :=

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

@@ -134,9 +134,7 @@ Case conversion may be inaccurate. Consider using '#align is_localization.of_le
 theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (algebraMap R S r)) :
     IsLocalization N S :=
   { map_units := fun r => h₂ r r.2
-    surj := fun s => by
-      obtain ⟨⟨x, y, hy⟩, H⟩ := IsLocalization.surj M s
-      exact ⟨⟨x, y, h₁ hy⟩, H⟩
+    surj := fun s => by obtain ⟨⟨x, y, hy⟩, H⟩ := IsLocalization.surj M s; exact ⟨⟨x, y, h₁ hy⟩, H⟩
     eq_iff_exists := fun x y => by
       constructor
       · rw [IsLocalization.eq_iff_exists M]
@@ -949,11 +947,7 @@ isomorphism `j : R ≃+* P` such that `j(M) = T` induces an isomorphism of local
 `S ≃+* Q`. -/
 @[simps]
 noncomputable def ringEquivOfRingEquiv (h : R ≃+* P) (H : M.map h.toMonoidHom = T) : S ≃+* Q :=
-  have H' : T.map h.symm.toMonoidHom = M :=
-    by
-    rw [← M.map_id, ← H, Submonoid.map_map]
-    congr
-    ext
+  have H' : T.map h.symm.toMonoidHom = M := by rw [← M.map_id, ← H, Submonoid.map_map]; congr ; ext;
     apply h.symm_apply_apply
   {
     map Q (h : R →+* P)
@@ -963,13 +957,11 @@ noncomputable def ringEquivOfRingEquiv (h : R ≃+* P) (H : M.map h.toMonoidHom
     left_inv := fun x =>
       by
       rw [map_map, map_unique _ (RingHom.id _), RingHom.id_apply]
-      intro x
-      convert congr_arg (algebraMap R S) (h.symm_apply_apply x).symm
+      intro x; convert congr_arg (algebraMap R S) (h.symm_apply_apply x).symm
     right_inv := fun x =>
       by
       rw [map_map, map_unique _ (RingHom.id _), RingHom.id_apply]
-      intro x
-      convert congr_arg (algebraMap P Q) (h.apply_symm_apply x).symm }
+      intro x; convert congr_arg (algebraMap P Q) (h.apply_symm_apply x).symm }
 #align is_localization.ring_equiv_of_ring_equiv IsLocalization.ringEquivOfRingEquiv
 
 end
@@ -1232,10 +1224,8 @@ instance : Add (Localization M) :=
 /- warning: localization.add_mk -> Localization.add_mk is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align localization.add_mk Localization.add_mkₓ'. -/
-theorem add_mk (a b c d) : (mk a b : Localization M) + mk c d = mk (b * c + d * a) (b * d) :=
-  by
-  unfold Add.add Localization.add
-  apply lift_on₂_mk
+theorem add_mk (a b c d) : (mk a b : Localization M) + mk c d = mk (b * c + d * a) (b * d) := by
+  unfold Add.add Localization.add; apply lift_on₂_mk
 #align localization.add_mk Localization.add_mk
 
 /- warning: localization.add_mk_self -> Localization.add_mk_self is a dubious translation:
@@ -1372,14 +1362,10 @@ instance {S : Type _} [Semiring S] [Module S R] [IsScalarTower S R R] : Module S
     Localization.distribMulAction with
     zero_smul :=
       Localization.ind <|
-        Prod.rec <| by
-          intros
-          simp only [Localization.smul_mk, zero_smul, mk_zero]
+        Prod.rec <| by intros ; simp only [Localization.smul_mk, zero_smul, mk_zero]
     add_smul := fun s₁ s₂ =>
       Localization.ind <|
-        Prod.rec <| by
-          intros
-          simp only [Localization.smul_mk, add_smul, add_mk_self] }
+        Prod.rec <| by intros ; simp only [Localization.smul_mk, add_smul, add_mk_self] }
 
 instance {S : Type _} [CommSemiring S] [Algebra S R] : Algebra S (Localization M)
     where
@@ -1572,9 +1558,7 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : 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)))))} (a : R) (b : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Neg.neg.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instNegLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) a) b)
 Case conversion may be inaccurate. Consider using '#align localization.neg_mk Localization.neg_mkₓ'. -/
-theorem neg_mk (a b) : -(mk a b : Localization M) = mk (-a) b :=
-  by
-  unfold Neg.neg Localization.neg
+theorem neg_mk (a b) : -(mk a b : Localization M) = mk (-a) b := by unfold Neg.neg Localization.neg;
   apply lift_on_mk
 #align localization.neg_mk Localization.neg_mk
 
@@ -1587,10 +1571,7 @@ instance : CommRing (Localization M) :=
       Localization.induction_on x fun x => by
         simp [smul_mk, add_mk_self, -mk_eq_monoid_of_mk', add_comm (n : ℤ) 1, add_smul]
     zsmul_neg' := fun n x =>
-      Localization.induction_on x fun x =>
-        by
-        rw [smul_mk, smul_mk, neg_mk, ← neg_smul]
-        rfl
+      Localization.induction_on x fun x => by rw [smul_mk, smul_mk, neg_mk, ← neg_smul]; rfl
     neg := Neg.neg
     sub := fun x y => x + -y
     sub_eq_add_neg := fun x y => rfl

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

@@ -170,10 +170,7 @@ abbrev toLocalizationMap : Submonoid.LocalizationMap M S :=
 -/
 
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(CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.to_localization_map_to_map IsLocalization.toLocalizationMap_toMapₓ'. -/
 @[simp]
 theorem toLocalizationMap_toMap : (toLocalizationMap M S).toMap = (algebraMap R S : R →*₀ S) :=
@@ -218,10 +215,7 @@ theorem toLocalizationMap_sec : (toLocalizationMap M S).sec = sec M :=
 #align is_localization.to_localization_map_sec IsLocalization.toLocalizationMap_sec
 
 /- warning: is_localization.sec_spec -> IsLocalization.sec_spec is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localization.sec_spec IsLocalization.sec_specₓ'. -/
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x` (so this lemma is true by definition). -/
@@ -231,10 +225,7 @@ theorem sec_spec (z : S) :
 #align is_localization.sec_spec IsLocalization.sec_spec
 
 /- warning: is_localization.sec_spec' -> IsLocalization.sec_spec' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_spec' IsLocalization.sec_spec'ₓ'. -/
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x`, so this lemma is just an application of `S`'s commutativity. -/
@@ -246,10 +237,7 @@ theorem sec_spec' (z : S) :
 variable {R M}
 
 /- warning: is_localization.map_right_cancel -> IsLocalization.map_right_cancel is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localization.map_right_cancel IsLocalization.map_right_cancelₓ'. -/
 theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap R S (c * y)) :
     algebraMap R S x = algebraMap R S y :=
@@ -257,10 +245,7 @@ theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap
 #align is_localization.map_right_cancel IsLocalization.map_right_cancel
 
 /- warning: is_localization.map_left_cancel -> IsLocalization.map_left_cancel is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_left_cancel IsLocalization.map_left_cancelₓ'. -/
 theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R S (y * c)) :
     algebraMap R S x = algebraMap R S y :=
@@ -268,10 +253,7 @@ theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R
 #align is_localization.map_left_cancel IsLocalization.map_left_cancel
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.eq_zero_of_fst_eq_zero IsLocalization.eq_zero_of_fst_eq_zeroₓ'. -/
 theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebraMap R S x)
     (hx : x = 0) : z = 0 := by
@@ -282,10 +264,7 @@ theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebra
 variable (M S)
 
 /- warning: is_localization.map_eq_zero_iff -> IsLocalization.map_eq_zero_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_eq_zero_iff IsLocalization.map_eq_zero_iffₓ'. -/
 theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r = 0 :=
   by
@@ -320,10 +299,7 @@ theorem mk'_sec (z : S) : mk' S (IsLocalization.sec M z).1 (IsLocalization.sec M
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul IsLocalization.mk'_mulₓ'. -/
 theorem mk'_mul (x₁ x₂ : R) (y₁ y₂ : M) : mk' S (x₁ * x₂) (y₁ * y₂) = mk' S x₁ y₁ * mk' S x₂ y₂ :=
   (toLocalizationMap M S).mk'_mul _ _ _ _
@@ -340,10 +316,7 @@ theorem mk'_one (x) : mk' S x (1 : M) = algebraMap R S x :=
 #align is_localization.mk'_one IsLocalization.mk'_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec IsLocalization.mk'_specₓ'. -/
 @[simp]
 theorem mk'_spec (x) (y : M) : mk' S x y * algebraMap R S y = algebraMap R S x :=
@@ -351,10 +324,7 @@ theorem mk'_spec (x) (y : M) : mk' S x y * algebraMap R S y = algebraMap R S x :
 #align is_localization.mk'_spec IsLocalization.mk'_spec
 
 /- warning: is_localization.mk'_spec' -> IsLocalization.mk'_spec' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec' IsLocalization.mk'_spec'ₓ'. -/
 @[simp]
 theorem mk'_spec' (x) (y : M) : algebraMap R S y * mk' S x y = algebraMap R S x :=
@@ -362,10 +332,7 @@ theorem mk'_spec' (x) (y : M) : algebraMap R S y * mk' S x y = algebraMap R S x
 #align is_localization.mk'_spec' IsLocalization.mk'_spec'
 
 /- warning: is_localization.mk'_spec_mk -> IsLocalization.mk'_spec_mk is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec_mk IsLocalization.mk'_spec_mkₓ'. -/
 @[simp]
 theorem mk'_spec_mk (x) (y : R) (hy : y ∈ M) :
@@ -374,10 +341,7 @@ theorem mk'_spec_mk (x) (y : R) (hy : y ∈ M) :
 #align is_localization.mk'_spec_mk IsLocalization.mk'_spec_mk
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec'_mk IsLocalization.mk'_spec'_mkₓ'. -/
 @[simp]
 theorem mk'_spec'_mk (x) (y : R) (hy : y ∈ M) :
@@ -388,10 +352,7 @@ theorem mk'_spec'_mk (x) (y : R) (hy : y ∈ M) :
 variable {S}
 
 /- warning: is_localization.eq_mk'_iff_mul_eq -> IsLocalization.eq_mk'_iff_mul_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localization.eq_mk'_iff_mul_eq IsLocalization.eq_mk'_iff_mul_eqₓ'. -/
 theorem eq_mk'_iff_mul_eq {x} {y : M} {z} :
     z = mk' S x y ↔ z * algebraMap R S y = algebraMap R S x :=
@@ -399,10 +360,7 @@ theorem eq_mk'_iff_mul_eq {x} {y : M} {z} :
 #align is_localization.eq_mk'_iff_mul_eq IsLocalization.eq_mk'_iff_mul_eq
 
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 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq_mul IsLocalization.mk'_eq_iff_eq_mulₓ'. -/
 theorem mk'_eq_iff_eq_mul {x} {y : M} {z} :
     mk' S x y = z ↔ algebraMap R S x = z * algebraMap R S y :=
@@ -410,10 +368,7 @@ theorem mk'_eq_iff_eq_mul {x} {y : M} {z} :
 #align is_localization.mk'_eq_iff_eq_mul IsLocalization.mk'_eq_iff_eq_mul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_add_eq_iff_add_mul_eq_mul IsLocalization.mk'_add_eq_iff_add_mul_eq_mulₓ'. -/
 theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
     mk' S x y + z₁ = z₂ ↔ algebraMap R S x + z₁ * algebraMap R S y = z₂ * algebraMap R S y := by
@@ -462,10 +417,7 @@ def uniqueOfZeroMem (h : (0 : R) ∈ M) : Unique S :=
 #align is_localization.unique_of_zero_mem IsLocalization.uniqueOfZeroMem
 
 /- warning: is_localization.mk'_eq_iff_eq -> IsLocalization.mk'_eq_iff_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq IsLocalization.mk'_eq_iff_eqₓ'. -/
 theorem mk'_eq_iff_eq {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (y₂ * x₁) = algebraMap R S (y₁ * x₂) :=
@@ -473,10 +425,7 @@ theorem mk'_eq_iff_eq {x₁ x₂} {y₁ y₂ : M} :
 #align is_localization.mk'_eq_iff_eq IsLocalization.mk'_eq_iff_eq
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq' IsLocalization.mk'_eq_iff_eq'ₓ'. -/
 theorem mk'_eq_iff_eq' {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (x₁ * y₂) = algebraMap R S (x₂ * y₁) :=
@@ -501,10 +450,7 @@ theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R
 #align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iff
 
 /- warning: is_localization.eq -> IsLocalization.eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.eq IsLocalization.eqₓ'. -/
 protected theorem eq {a₁ b₁} {a₂ b₂ : M} :
     mk' S a₁ a₂ = mk' S b₁ b₂ ↔ ∃ c : M, ↑c * (↑b₂ * a₁) = c * (a₂ * b₁) :=
@@ -512,10 +458,7 @@ protected theorem eq {a₁ b₁} {a₂ b₂ : M} :
 #align is_localization.eq IsLocalization.eq
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_zero_iff IsLocalization.mk'_eq_zero_iffₓ'. -/
 theorem mk'_eq_zero_iff (x : R) (s : M) : mk' S x s = 0 ↔ ∃ m : M, ↑m * x = 0 := by
   rw [← (map_units S s).mul_left_inj, mk'_spec, MulZeroClass.zero_mul, map_eq_zero_iff M]
@@ -549,10 +492,7 @@ section Ext
 variable [Algebra R P] [IsLocalization M P]
 
 /- warning: is_localization.eq_iff_eq -> IsLocalization.eq_iff_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.eq_iff_eq IsLocalization.eq_iff_eqₓ'. -/
 theorem eq_iff_eq {x y} :
     algebraMap R S x = algebraMap R S y ↔ algebraMap R P x = algebraMap R P y :=
@@ -571,10 +511,7 @@ theorem mk'_eq_iff_mk'_eq {x₁ x₂} {y₁ y₂ : M} :
 #align is_localization.mk'_eq_iff_mk'_eq IsLocalization.mk'_eq_iff_mk'_eq
 
 /- warning: is_localization.mk'_eq_of_eq -> IsLocalization.mk'_eq_of_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_of_eq IsLocalization.mk'_eq_of_eqₓ'. -/
 theorem mk'_eq_of_eq {a₁ b₁ : R} {a₂ b₂ : M} (H : ↑a₂ * b₁ = ↑b₂ * a₁) :
     mk' S a₁ a₂ = mk' S b₁ b₂ :=
@@ -582,10 +519,7 @@ theorem mk'_eq_of_eq {a₁ b₁ : R} {a₂ b₂ : M} (H : ↑a₂ * b₁ = ↑b
 #align is_localization.mk'_eq_of_eq IsLocalization.mk'_eq_of_eq
 
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 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_of_eq' IsLocalization.mk'_eq_of_eq'ₓ'. -/
 theorem mk'_eq_of_eq' {a₁ b₁ : R} {a₂ b₂ : M} (H : b₁ * ↑a₂ = a₁ * ↑b₂) :
     mk' S a₁ a₂ = mk' S b₁ b₂ :=
@@ -606,10 +540,7 @@ theorem mk'_self {x : R} (hx : x ∈ M) : mk' S x ⟨x, hx⟩ = 1 :=
 #align is_localization.mk'_self IsLocalization.mk'_self
 
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 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_self' IsLocalization.mk'_self'ₓ'. -/
 @[simp]
 theorem mk'_self' {x : M} : mk' S (x : R) x = 1 :=
@@ -650,10 +581,7 @@ theorem mk'_eq_mul_mk'_one (x : R) (y : M) : mk' S x y = (algebraMap R S) x * mk
 #align is_localization.mk'_eq_mul_mk'_one IsLocalization.mk'_eq_mul_mk'_one
 
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 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_cancel_left IsLocalization.mk'_mul_cancel_leftₓ'. -/
 @[simp]
 theorem mk'_mul_cancel_left (x : R) (y : M) : mk' S (y * x : R) y = (algebraMap R S) x :=
@@ -661,20 +589,14 @@ theorem mk'_mul_cancel_left (x : R) (y : M) : mk' S (y * x : R) y = (algebraMap
 #align is_localization.mk'_mul_cancel_left IsLocalization.mk'_mul_cancel_left
 
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 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_cancel_right IsLocalization.mk'_mul_cancel_rightₓ'. -/
 theorem mk'_mul_cancel_right (x : R) (y : M) : mk' S (x * y) y = (algebraMap R S) x :=
   (toLocalizationMap M S).mk'_mul_cancel_right _ _
 #align is_localization.mk'_mul_cancel_right IsLocalization.mk'_mul_cancel_right
 
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 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_mk'_eq_one IsLocalization.mk'_mul_mk'_eq_oneₓ'. -/
 @[simp]
 theorem mk'_mul_mk'_eq_one (x y : M) : mk' S (x : R) y * mk' S (y : R) x = 1 := by
@@ -682,10 +604,7 @@ theorem mk'_mul_mk'_eq_one (x y : M) : mk' S (x : R) y * mk' S (y : R) x = 1 :=
 #align is_localization.mk'_mul_mk'_eq_one IsLocalization.mk'_mul_mk'_eq_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_mk'_eq_one' IsLocalization.mk'_mul_mk'_eq_one'ₓ'. -/
 theorem mk'_mul_mk'_eq_one' (x : R) (y : M) (h : x ∈ M) : mk' S x y * mk' S (y : R) ⟨x, h⟩ = 1 :=
   mk'_mul_mk'_eq_one ⟨x, h⟩ _
@@ -696,10 +615,7 @@ section
 variable (M)
 
 /- warning: is_localization.is_unit_comp -> IsLocalization.isUnit_comp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.is_unit_comp IsLocalization.isUnit_compₓ'. -/
 theorem isUnit_comp (j : S →+* P) (y : M) : IsUnit (j.comp (algebraMap R S) y) :=
   (toLocalizationMap M S).isUnit_comp j.toMonoidHom _
@@ -708,10 +624,7 @@ theorem isUnit_comp (j : S →+* P) (y : M) : IsUnit (j.comp (algebraMap R S) y)
 end
 
 /- warning: is_localization.eq_of_eq -> IsLocalization.eq_of_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.eq_of_eq IsLocalization.eq_of_eqₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g(M) ⊆ units P`, `f x = f y → g x = g y` for all `x y : R`. -/
@@ -721,10 +634,7 @@ theorem eq_of_eq {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) {x y}
 #align is_localization.eq_of_eq IsLocalization.eq_of_eq
 
 /- warning: is_localization.mk'_add -> IsLocalization.mk'_add is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_add IsLocalization.mk'_addₓ'. -/
 theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
     mk' S (x₁ * y₂ + x₂ * y₁) (y₁ * y₂) = mk' S x₁ y₁ + mk' S x₂ y₂ :=
@@ -739,10 +649,7 @@ theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
 #align is_localization.mk'_add IsLocalization.mk'_add
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mul_add_inv_left IsLocalization.mul_add_inv_leftₓ'. -/
 theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (w z₁ z₂ : P) :
     w * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) h y)⁻¹ + z₁ = z₂ ↔ w + g y * z₁ = g y * z₂ :=
@@ -754,10 +661,7 @@ theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (
 #align is_localization.mul_add_inv_left IsLocalization.mul_add_inv_left
 
 /- warning: is_localization.lift_spec_mul_add -> IsLocalization.lift_spec_mul_add is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align is_localization.lift_spec_mul_add IsLocalization.lift_spec_mul_addₓ'. -/
 theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w' v) :
     ((toLocalizationWithZeroMap M S).lift g.toMonoidWithZeroHom hg) z * w + w' = v ↔
@@ -770,10 +674,7 @@ theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w'
 #align is_localization.lift_spec_mul_add IsLocalization.lift_spec_mul_add
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift IsLocalization.liftₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
@@ -798,10 +699,7 @@ noncomputable def lift {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) : S →+*
 variable {g : R →+* P} (hg : ∀ y : M, IsUnit (g y))
 
 /- warning: is_localization.lift_mk' -> IsLocalization.lift_mk' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk' IsLocalization.lift_mk'ₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
@@ -812,20 +710,14 @@ theorem lift_mk' (x y) :
 #align is_localization.lift_mk' IsLocalization.lift_mk'
 
 /- warning: is_localization.lift_mk'_spec -> IsLocalization.lift_mk'_spec is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk'_spec IsLocalization.lift_mk'_specₓ'. -/
 theorem lift_mk'_spec (x v) (y : M) : lift hg (mk' S x y) = v ↔ g x = g y * v :=
   (toLocalizationMap M S).lift_mk'_spec _ _ _ _
 #align is_localization.lift_mk'_spec IsLocalization.lift_mk'_spec
 
 /- warning: is_localization.lift_eq -> IsLocalization.lift_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_eq IsLocalization.lift_eqₓ'. -/
 @[simp]
 theorem lift_eq (x : R) : lift hg ((algebraMap R S) x) = g x :=
@@ -833,10 +725,7 @@ theorem lift_eq (x : R) : lift hg ((algebraMap R S) x) = g x :=
 #align is_localization.lift_eq IsLocalization.lift_eq
 
 /- warning: is_localization.lift_eq_iff -> IsLocalization.lift_eq_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_eq_iff IsLocalization.lift_eq_iffₓ'. -/
 theorem lift_eq_iff {x y : R × M} :
     lift hg (mk' S x.1 x.2) = lift hg (mk' S y.1 y.2) ↔ g (x.1 * y.2) = g (y.1 * x.2) :=
@@ -844,10 +733,7 @@ theorem lift_eq_iff {x y : R × M} :
 #align is_localization.lift_eq_iff IsLocalization.lift_eq_iff
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_comp IsLocalization.lift_compₓ'. -/
 @[simp]
 theorem lift_comp : (lift hg).comp (algebraMap R S) = g :=
@@ -868,10 +754,7 @@ theorem lift_of_comp (j : S →+* P) : lift (isUnit_comp M j) = j :=
 variable (M)
 
 /- warning: is_localization.monoid_hom_ext -> IsLocalization.monoidHom_ext is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localization.monoid_hom_ext IsLocalization.monoidHom_extₓ'. -/
 /-- See note [partially-applied ext lemmas] -/
 theorem monoidHom_ext ⦃j k : S →* P⦄
@@ -906,10 +789,7 @@ theorem algHom_subsingleton [Algebra R P] : Subsingleton (S →ₐ[R] P) :=
 #align is_localization.alg_hom_subsingleton IsLocalization.algHom_subsingleton
 
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 Case conversion may be inaccurate. Consider using '#align is_localization.ext IsLocalization.extₓ'. -/
 /-- To show `j` and `k` agree on the whole localization, it suffices to show they agree
 on the image of the base ring, if they preserve `1` and `*`. -/
@@ -922,10 +802,7 @@ protected theorem ext (j k : S → P) (hj1 : j 1 = 1) (hk1 : k 1 = 1)
 variable {M}
 
 /- warning: is_localization.lift_unique -> IsLocalization.lift_unique is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_unique IsLocalization.lift_uniqueₓ'. -/
 theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) : lift hg = j :=
   RingHom.ext <|
@@ -946,10 +823,7 @@ theorem lift_id (x) : lift (map_units S : ∀ y : M, IsUnit _) x = x :=
 #align is_localization.lift_id IsLocalization.lift_id
 
 /- warning: is_localization.lift_surjective_iff -> IsLocalization.lift_surjective_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_surjective_iff IsLocalization.lift_surjective_iffₓ'. -/
 theorem lift_surjective_iff :
     Surjective (lift hg : S → P) ↔ ∀ v : P, ∃ x : R × M, v * g x.2 = g x.1 :=
@@ -957,10 +831,7 @@ theorem lift_surjective_iff :
 #align is_localization.lift_surjective_iff IsLocalization.lift_surjective_iff
 
 /- warning: is_localization.lift_injective_iff -> IsLocalization.lift_injective_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_injective_iff IsLocalization.lift_injective_iffₓ'. -/
 theorem lift_injective_iff :
     Injective (lift hg : S → P) ↔ ∀ x y, algebraMap R S x = algebraMap R S y ↔ g x = g y :=
@@ -978,10 +849,7 @@ section
 variable (Q)
 
 /- warning: is_localization.map -> IsLocalization.map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map IsLocalization.mapₓ'. -/
 /-- Map a homomorphism `g : R →+* P` to `S →+* Q`, where `S` and `Q` are
 localizations of `R` and `P` at `M` and `T` respectively,
@@ -996,20 +864,14 @@ noncomputable def map (g : R →+* P) (hy : M ≤ T.comap g) : S →+* Q :=
 end
 
 /- warning: is_localization.map_eq -> IsLocalization.map_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localization.map_eq IsLocalization.map_eqₓ'. -/
 theorem map_eq (x) : map Q g hy ((algebraMap R S) x) = algebraMap P Q (g x) :=
   lift_eq (fun y => map_units _ ⟨g y, hy y.2⟩) x
 #align is_localization.map_eq IsLocalization.map_eq
 
 /- warning: is_localization.map_comp -> IsLocalization.map_comp is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localization.map_comp IsLocalization.map_compₓ'. -/
 @[simp]
 theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g :=
@@ -1017,10 +879,7 @@ theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g
 #align is_localization.map_comp IsLocalization.map_comp
 
 /- warning: is_localization.map_mk' -> IsLocalization.map_mk' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_mk' IsLocalization.map_mk'ₓ'. -/
 theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.2⟩ :=
   @Submonoid.LocalizationMap.map_mk' _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom _
@@ -1028,10 +887,7 @@ theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.
 #align is_localization.map_mk' IsLocalization.map_mk'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_id IsLocalization.map_idₓ'. -/
 @[simp]
 theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
@@ -1040,10 +896,7 @@ theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
 #align is_localization.map_id IsLocalization.map_id
 
 /- warning: is_localization.map_unique -> IsLocalization.map_unique is a dubious translation:
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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))) -> (Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (IsLocalization.map.{u2, u4, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_unique IsLocalization.map_uniqueₓ'. -/
 theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algebraMap P Q (g x)) :
     map Q g hy = j :=
@@ -1051,10 +904,7 @@ theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algeb
 #align is_localization.map_unique IsLocalization.map_unique
 
 /- warning: is_localization.map_comp_map -> IsLocalization.map_comp_map is a dubious translation:
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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toHasLe.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)), Eq.{max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (RingHom.comp.{u2, u4, u6} S Q W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) 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(CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx)))
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(NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u2} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)), Eq.{max (succ u3) (succ u5)} (RingHom.{u3, u5} S W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHom.comp.{u3, u2, u5} S Q W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (IsLocalization.map.{u4, u2, u6, u5} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u3, u4, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u3, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_comp_map IsLocalization.map_comp_mapₓ'. -/
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
@@ -1067,10 +917,7 @@ theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSe
 #align is_localization.map_comp_map IsLocalization.map_comp_map
 
 /- warning: is_localization.map_map -> IsLocalization.map_map is a dubious translation:
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(Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u3} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_map IsLocalization.map_mapₓ'. -/
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
@@ -1081,10 +928,7 @@ theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemirin
 #align is_localization.map_map IsLocalization.map_map
 
 /- warning: is_localization.map_smul -> IsLocalization.map_smul is a dubious translation:
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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_smul IsLocalization.map_smulₓ'. -/
 theorem map_smul (x : S) (z : R) : map Q g hy (z • x : S) = g z • map Q g hy x := by
   rw [Algebra.smul_def, Algebra.smul_def, RingHom.map_mul, map_eq]
@@ -1131,10 +975,7 @@ noncomputable def ringEquivOfRingEquiv (h : R ≃+* P) (H : M.map h.toMonoidHom
 end
 
 /- warning: is_localization.ring_equiv_of_ring_equiv_eq_map -> IsLocalization.ringEquivOfRingEquiv_eq_map is a dubious translation:
-lean 3 declaration is
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(Distrib.toAdd.{u1} Q (NonUnitalNonAssocSemiring.toDistrib.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)) (RingEquivClass.toRingHomClass.{max u2 u1, u2, u1} (RingEquiv.{u2, u1} S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))) (Distrib.toAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) 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(NonUnitalNonAssocSemiring.toDistrib.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6))))))) (IsLocalization.ringEquivOfRingEquiv.{u4, u2, u3, u1} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 j H)) (IsLocalization.map.{u4, u2, u3, u1} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 (RingHomClass.toRingHom.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquivClass.toRingHomClass.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) j) (Submonoid.le_comap_of_map_le.{max u4 u3, u4, u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) T (RingHomClass.toRingHom.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquivClass.toRingHomClass.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) j) (le_of_eq.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toRingHom.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquivClass.toRingHomClass.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) j) M) T H)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_eq_map IsLocalization.ringEquivOfRingEquiv_eq_mapₓ'. -/
 theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T) :
     (ringEquivOfRingEquiv S Q j H : S →+* Q) =
@@ -1143,10 +984,7 @@ theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T
 #align is_localization.ring_equiv_of_ring_equiv_eq_map IsLocalization.ringEquivOfRingEquiv_eq_map
 
 /- warning: is_localization.ring_equiv_of_ring_equiv_eq -> IsLocalization.ringEquivOfRingEquiv_eq is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eqₓ'. -/
 @[simp]
 theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x) :
@@ -1155,10 +993,7 @@ theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x
 #align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eq
 
 /- warning: is_localization.ring_equiv_of_ring_equiv_mk' -> IsLocalization.ringEquivOfRingEquiv_mk' is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_mk' IsLocalization.ringEquivOfRingEquiv_mk'ₓ'. -/
 theorem ringEquivOfRingEquiv_mk' {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x : R) (y : M) :
     ringEquivOfRingEquiv S Q j H (mk' S x y) =
@@ -1189,10 +1024,7 @@ noncomputable def algEquiv : S ≃ₐ[R] Q :=
 end
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
@@ -1200,10 +1032,7 @@ theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
 #align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.alg_equiv_symm_mk' IsLocalization.algEquiv_symm_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) = mk' S x y :=
@@ -1401,10 +1230,7 @@ instance : Add (Localization M) :=
   ⟨Localization.add⟩
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localization.add_mk Localization.add_mkₓ'. -/
 theorem add_mk (a b c d) : (mk a b : Localization M) + mk c d = mk (b * c + d * a) (b * d) :=
   by
@@ -1429,7 +1255,6 @@ theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b
 /- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
 private unsafe def tac :=
   sorry
-#align localization.tac localization.tac
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
@@ -1601,20 +1426,14 @@ theorem toLocalizationMap_eq_monoidOf : toLocalizationMap M (Localization M) = m
 #align localization.to_localization_map_eq_monoid_of Localization.toLocalizationMap_eq_monoidOf
 
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 Case conversion may be inaccurate. Consider using '#align localization.monoid_of_eq_algebra_map Localization.monoidOf_eq_algebraMapₓ'. -/
 theorem monoidOf_eq_algebraMap (x) : (monoidOf M).toMap x = algebraMap R (Localization M) x :=
   rfl
 #align localization.monoid_of_eq_algebra_map Localization.monoidOf_eq_algebraMap
 
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 Case conversion may be inaccurate. Consider using '#align localization.mk_one_eq_algebra_map Localization.mk_one_eq_algebraMapₓ'. -/
 theorem mk_one_eq_algebraMap (x) : mk x 1 = algebraMap R (Localization M) x :=
   rfl
@@ -1642,10 +1461,7 @@ theorem mk_eq_mk' : (mk : R → M → Localization M) = IsLocalization.mk' (Loca
 #align localization.mk_eq_mk' Localization.mk_eq_mk'
 
 /- warning: localization.mk_algebra_map -> Localization.mk_algebraMap is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localization.mk_algebra_map Localization.mk_algebraMapₓ'. -/
 theorem mk_algebraMap {A : Type _} [CommSemiring A] [Algebra A R] (m : A) :
     mk (algebraMap A R m) 1 = algebraMap A (Localization M) m := by
@@ -1692,10 +1508,7 @@ noncomputable def IsLocalization.unique (R Rₘ) [CommSemiring R] [CommSemiring
 end
 
 /- warning: localization.alg_equiv_mk' -> Localization.algEquiv_mk' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_mk' Localization.algEquiv_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) = mk' S x y :=
@@ -1703,10 +1516,7 @@ theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) =
 #align localization.alg_equiv_mk' Localization.algEquiv_mk'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_symm_mk' Localization.algEquiv_symm_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) :
@@ -1715,19 +1525,13 @@ theorem algEquiv_symm_mk' (x : R) (y : M) :
 #align localization.alg_equiv_symm_mk' Localization.algEquiv_symm_mk'
 
 /- warning: localization.alg_equiv_mk -> Localization.algEquiv_mk is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_mk Localization.algEquiv_mkₓ'. -/
 theorem algEquiv_mk (x y) : algEquiv M S (mk x y) = mk' S x y := by rw [mk_eq_mk', alg_equiv_mk']
 #align localization.alg_equiv_mk Localization.algEquiv_mk
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_symm_mk Localization.algEquiv_symm_mkₓ'. -/
 theorem algEquiv_symm_mk (x : R) (y : M) : (algEquiv M S).symm (mk' S x y) = mk x y := by
   rw [mk_eq_mk', alg_equiv_symm_mk']
@@ -1800,10 +1604,7 @@ instance : CommRing (Localization M) :=
           ring) }
 
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 Case conversion may be inaccurate. Consider using '#align localization.sub_mk Localization.sub_mkₓ'. -/
 theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b * c) (b * d) :=
   calc
@@ -1860,10 +1661,7 @@ protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraM
 #align is_localization.injective IsLocalization.injective
 
 /- warning: is_localization.to_map_ne_zero_of_mem_non_zero_divisors -> IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisors is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.to_map_ne_zero_of_mem_non_zero_divisors IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisorsₓ'. -/
 protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M ≤ nonZeroDivisors R)
     {x : R} (hx : x ∈ nonZeroDivisors R) : algebraMap R S x ≠ 0 :=
@@ -1874,10 +1672,7 @@ protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M 
 variable {S}
 
 /- warning: is_localization.sec_snd_ne_zero -> IsLocalization.sec_snd_ne_zero is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_localization.sec_snd_ne_zero IsLocalization.sec_snd_ne_zeroₓ'. -/
 theorem sec_snd_ne_zero [Nontrivial R] (hM : M ≤ nonZeroDivisors R) (x : S) :
     ((sec M x).snd : R) ≠ 0 :=
@@ -1885,10 +1680,7 @@ theorem sec_snd_ne_zero [Nontrivial R] (hM : M ≤ nonZeroDivisors R) (x : S) :
 #align is_localization.sec_snd_ne_zero IsLocalization.sec_snd_ne_zero
 
 /- warning: is_localization.sec_fst_ne_zero -> IsLocalization.sec_fst_ne_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zeroₓ'. -/
 theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDivisors R) {x : S}
     (hx : x ≠ 0) : (sec M x).fst ≠ 0 :=
@@ -1903,10 +1695,7 @@ theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDiv
 variable (S M) (Q : Type _) [CommRing Q] {g : R →+* P} [Algebra P Q]
 
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-lean 3 declaration is
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(CommRing.toRing.{u4} Q _inst_6))], (Function.Injective.{succ u1, succ u3} R P (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (fun (_x : RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u4} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7], Function.Injective.{succ u2, succ u4} S Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (IsLocalization.map.{u1, u2, u3, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
-but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] (Q : Type.{u2}) [_inst_6 : CommRing.{u2} Q] {g : RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u2} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))], (Function.Injective.{succ u4, succ u3} R P (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (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} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u2} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7], Function.Injective.{succ u1, succ u2} S Q (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))) (RingHom.instRingHomClassRingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))))) (IsLocalization.map.{u4, u1, u3, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{max u4 u3, u3, u4} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injectiveₓ'. -/
 /-- Injectivity of a map descends to the map induced on localizations. -/
 theorem map_injective_of_injective (hg : Function.Injective g)
@@ -2071,10 +1860,7 @@ variable (S Rₘ Sₘ)
 include S
 
 /- warning: is_localization.map_units_map_submonoid -> IsLocalization.map_units_map_submonoid is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Sₘ : Type.{u3}) [_inst_6 : CommRing.{u3} Sₘ] [_inst_9 : Algebra.{u2, u3} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u3} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u1, u2, u3} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} S Sₘ (AddZeroClass.toHasZero.{u3} 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-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] (Sₘ : Type.{u1}) [_inst_6 : CommRing.{u1} Sₘ] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u2, u3, u1} R S Sₘ (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) (Algebra.toSMul.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_12)] (y : 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 M)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_12) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoidₓ'. -/
 theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R Sₘ y) :=
   by
@@ -2083,10 +1869,7 @@ theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R S
 #align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoid
 
 /- warning: is_localization.algebra_map_mk' -> IsLocalization.algebraMap_mk' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} 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(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 M))))) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M y)))
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-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u4, u2, u3} R Rₘ Sₘ (Algebra.toSMul.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u4, u1, u3} R S Sₘ (Algebra.toSMul.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] (x : R) (y : 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 M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))))))) (algebraMap.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u1, u3} ((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_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2))))))) x_1 (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S 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(CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (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)))))) M)) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u4} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M y)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_mk' IsLocalization.algebraMap_mk'ₓ'. -/
 @[simp]
 theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
@@ -2104,10 +1887,7 @@ theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
 variable (M)
 
 /- warning: is_localization.algebra_map_eq_map_map_submonoid -> IsLocalization.algebraMap_eq_map_map_submonoid is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))], Eq.{max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u4}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u4} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u4, u3} R Rₘ Sₘ (Algebra.toSMul.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u3} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u4} Rₘ (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (algebraMap.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u2, u4, u1, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3))]))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_eq_map_map_submonoid IsLocalization.algebraMap_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
@@ -2126,10 +1906,7 @@ theorem IsLocalization.algebraMap_eq_map_map_submonoid :
 #align is_localization.algebra_map_eq_map_map_submonoid IsLocalization.algebraMap_eq_map_map_submonoid
 
 /- warning: is_localization.algebra_map_apply_eq_map_map_submonoid -> IsLocalization.algebraMap_apply_eq_map_map_submonoid is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : Rₘ), Eq.{succ u4} Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ 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S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) 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(Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))) x)
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u4} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u3, u4} R Rₘ Sₘ (Algebra.toSMul.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u4} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] (x : Rₘ), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (IsLocalization.map.{u2, u3, u1, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3))])) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
@@ -2148,10 +1925,7 @@ theorem IsLocalization.algebraMap_apply_eq_map_map_submonoid (x) :
 variable {R}
 
 /- warning: is_localization.lift_algebra_map_eq_algebra_map -> IsLocalization.lift_algebraMap_eq_algebraMap is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))], Eq.{max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (IsLocalization.lift.{u1, u3, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_8 (algebraMap.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12) (IsLocalization.map_units_map_submonoid.{u1, u2, u4} R _inst_1 M S _inst_2 _inst_3 Sₘ _inst_6 _inst_9 _inst_10 _inst_12 _inst_14)) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11)
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u4}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u4} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u4, u3} R Rₘ Sₘ (Algebra.toSMul.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u3} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u4} Rₘ (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (IsLocalization.lift.{u2, u4, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7 Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_8 (algebraMap.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12) (IsLocalization.map_units_map_submonoid.{u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Sₘ _inst_6 _inst_9 _inst_10 _inst_12 _inst_14)) (algebraMap.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_algebra_map_eq_algebra_map IsLocalization.lift_algebraMap_eq_algebraMapₓ'. -/
 theorem IsLocalization.lift_algebraMap_eq_algebraMap :
     @IsLocalization.lift R _ M Rₘ _ _ Sₘ _ _ (algebraMap R Sₘ)
@@ -2165,10 +1939,7 @@ end
 variable (Rₘ Sₘ)
 
 /- warning: localization_algebra_injective -> localizationAlgebra_injective is a dubious translation:
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(CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))))))) (algebraMap.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} S 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+<too large>
 Case conversion may be inaccurate. Consider using '#align localization_algebra_injective localizationAlgebra_injectiveₓ'. -/
 /-- Injectivity of the underlying `algebra_map` descends to the algebra induced by localization. -/
 theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)) :

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

@@ -1192,7 +1192,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] [_inst_7 : Algebra.{u1, u3} R Q _inst_1 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} R _inst_1 M Q _inst_6 _inst_7] (x : R) (y : 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)))))) M), Eq.{succ u3} Q (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgEquiv.{u1, u2, u3} R S Q _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u3} Q _inst_6) _inst_3 _inst_7) (fun (_x : AlgEquiv.{u1, u2, u3} R S Q _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u3} Q _inst_6) _inst_3 _inst_7) => S -> Q) (AlgEquiv.hasCoeToFun.{u1, u2, u3} R S Q _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u3} Q _inst_6) _inst_3 _inst_7) (IsLocalization.algEquiv.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 _inst_5 Q _inst_6 _inst_7 _inst_8) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u1, u3} R _inst_1 M Q _inst_6 _inst_7 _inst_8 x y)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} R Q _inst_1 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} R _inst_1 M Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => Q) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => Q) _x) (SMulHomClass.toFunLike.{max u1 u2, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) R S Q (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 _inst_2)))))) (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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u1} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u3, u1} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} R Q (AddMonoid.toZero.{u2} Q (AddCommMonoid.toAddMonoid.{u2} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))) (DistribSMul.toSMulZeroClass.{u3, u2} R Q (AddMonoid.toAddZeroClass.{u2} Q (AddCommMonoid.toAddMonoid.{u2} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))) (DistribMulAction.toDistribSMul.{u3, u2} R Q (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))))) (Module.toDistribMulAction.{u3, u2} R Q (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Algebra.toModule.{u3, u2} R Q _inst_1 (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) R S Q (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (AddCommMonoid.toAddMonoid.{u2} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))))) (Module.toDistribMulAction.{u3, u1} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (Module.toDistribMulAction.{u3, u2} R Q (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Algebra.toModule.{u3, u2} R Q _inst_1 (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u1 u2} R S Q (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Algebra.toModule.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Algebra.toModule.{u3, u2} R Q _inst_1 (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_7) (AlgHomClass.linearMapClass.{u3, u1, u2, max u1 u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7 (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) (AlgEquivClass.toAlgHomClass.{max u1 u2, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7)))))) (IsLocalization.algEquiv.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 Q _inst_6 _inst_7 _inst_8) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u3, u2} R _inst_1 M Q _inst_6 _inst_7 _inst_8 x y)
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} R Q _inst_1 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} R _inst_1 M Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => Q) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => Q) _x) (SMulHomClass.toFunLike.{max u1 u2, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) R S Q (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 _inst_2)))))) (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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u1} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u3, u1} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} R Q (AddMonoid.toZero.{u2} Q (AddCommMonoid.toAddMonoid.{u2} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))) (DistribSMul.toSMulZeroClass.{u3, u2} R Q (AddMonoid.toAddZeroClass.{u2} Q (AddCommMonoid.toAddMonoid.{u2} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))) (DistribMulAction.toDistribSMul.{u3, u2} R Q (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))))) (Module.toDistribMulAction.{u3, u2} R Q (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Algebra.toModule.{u3, u2} R Q _inst_1 (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) R S Q (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (AddCommMonoid.toAddMonoid.{u2} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))))) (Module.toDistribMulAction.{u3, u1} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (Module.toDistribMulAction.{u3, u2} R Q (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Algebra.toModule.{u3, u2} R Q _inst_1 (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u1 u2} R S Q (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Algebra.toModule.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Algebra.toModule.{u3, u2} R Q _inst_1 (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_7) (AlgHomClass.linearMapClass.{u3, u1, u2, max u1 u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7 (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) (AlgEquivClass.toAlgHomClass.{max u1 u2, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7) R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u1, u2} R S Q _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_3 _inst_7)))))) (IsLocalization.algEquiv.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 Q _inst_6 _inst_7 _inst_8) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u3, u2} R _inst_1 M Q _inst_6 _inst_7 _inst_8 x y)
 Case conversion may be inaccurate. Consider using '#align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
@@ -1203,7 +1203,7 @@ theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] [_inst_7 : Algebra.{u1, u3} R Q _inst_1 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} R _inst_1 M Q _inst_6 _inst_7] (x : R) (y : 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)))))) M), Eq.{succ u2} S (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (AlgEquiv.{u1, u3, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u3} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) (fun (_x : AlgEquiv.{u1, u3, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u3} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) => Q -> S) (AlgEquiv.hasCoeToFun.{u1, u3, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u3} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) (AlgEquiv.symm.{u1, u2, u3} R S Q _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u3} Q _inst_6) _inst_3 _inst_7 (IsLocalization.algEquiv.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 _inst_5 Q _inst_6 _inst_7 _inst_8)) (IsLocalization.mk'.{u1, u3} R _inst_1 M Q _inst_6 _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {Q : Type.{u1}} [_inst_6 : CommSemiring.{u1} Q] [_inst_7 : Algebra.{u3, u1} R Q _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u1} R _inst_1 M Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Q) => S) (IsLocalization.mk'.{u3, u1} R _inst_1 M Q _inst_6 _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) Q (fun (_x : Q) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Q) => S) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) R Q S (SMulZeroClass.toSMul.{u3, u1} R Q (AddMonoid.toZero.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))))) (DistribSMul.toSMulZeroClass.{u3, u1} R Q (AddMonoid.toAddZeroClass.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))))) (DistribMulAction.toDistribSMul.{u3, u1} R Q (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6))))) (Module.toDistribMulAction.{u3, u1} R Q (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))) (Algebra.toModule.{u3, u1} R Q _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) _inst_7))))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u2} R S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u2} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) R Q S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6))))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u3, u1} R Q (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))) (Algebra.toModule.{u3, u1} R Q _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) _inst_7)) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R Q S (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u3, u1} R Q _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) _inst_7) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (AlgHomClass.linearMapClass.{u3, u1, u2, max u2 u1} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3 (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3)))))) (AlgEquiv.symm.{u3, u2, u1} R S Q _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} Q _inst_6) _inst_3 _inst_7 (IsLocalization.algEquiv.{u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 Q _inst_6 _inst_7 _inst_8)) (IsLocalization.mk'.{u3, u1} R _inst_1 M Q _inst_6 _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u3, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {Q : Type.{u1}} [_inst_6 : CommSemiring.{u1} Q] [_inst_7 : Algebra.{u3, u1} R Q _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u1} R _inst_1 M Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Q) => S) (IsLocalization.mk'.{u3, u1} R _inst_1 M Q _inst_6 _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) Q (fun (_x : Q) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Q) => S) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) R Q S (SMulZeroClass.toSMul.{u3, u1} R Q (AddMonoid.toZero.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))))) (DistribSMul.toSMulZeroClass.{u3, u1} R Q (AddMonoid.toAddZeroClass.{u1} Q (AddCommMonoid.toAddMonoid.{u1} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))))) (DistribMulAction.toDistribSMul.{u3, u1} R Q (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6))))) (Module.toDistribMulAction.{u3, u1} R Q (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))) (Algebra.toModule.{u3, u1} R Q _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) _inst_7))))) (SMulZeroClass.toSMul.{u3, u2} R S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u2} R S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u2} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) R Q S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6))))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u3, u1} R Q (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))) (Algebra.toModule.{u3, u1} R Q _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) _inst_7)) (Module.toDistribMulAction.{u3, u2} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R Q S (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Q (Semiring.toNonAssocSemiring.{u1} Q (CommSemiring.toSemiring.{u1} Q _inst_6)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u3, u1} R Q _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) _inst_7) (Algebra.toModule.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (AlgHomClass.linearMapClass.{u3, u1, u2, max u2 u1} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3 (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3) R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u1, u2} R Q S _inst_1 (CommSemiring.toSemiring.{u1} Q _inst_6) (CommSemiring.toSemiring.{u2} S _inst_2) _inst_7 _inst_3)))))) (AlgEquiv.symm.{u3, u2, u1} R S Q _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} Q _inst_6) _inst_3 _inst_7 (IsLocalization.algEquiv.{u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 Q _inst_6 _inst_7 _inst_8)) (IsLocalization.mk'.{u3, u1} R _inst_1 M Q _inst_6 _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u3, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
 Case conversion may be inaccurate. Consider using '#align is_localization.alg_equiv_symm_mk' IsLocalization.algEquiv_symm_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) = mk' S x y :=
@@ -1695,7 +1695,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgEquiv.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) => (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) -> S) (AlgEquiv.hasCoeToFun.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (Localization.algEquiv.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M) x y)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.isLocalization.{u2} R _inst_1 M) x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (fun (_x : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (SMulZeroClass.toSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toZero.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toAddZeroClass.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u2, u2, u1, max u2 u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (AlgHomClass.linearMapClass.{u2, u2, u1, max u2 u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3)))))) (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.isLocalization.{u2} R _inst_1 M) x y)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.isLocalization.{u2} R _inst_1 M) x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (fun (_x : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (SMulZeroClass.toSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toZero.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u2, u2, u1, max u2 u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (AlgHomClass.linearMapClass.{u2, u2, u1, max u2 u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3)))))) (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.isLocalization.{u2} R _inst_1 M) x y)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_mk' Localization.algEquiv_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) = mk' S x y :=
@@ -1706,7 +1706,7 @@ theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgEquiv.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgEquiv.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) => S -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (AlgEquiv.hasCoeToFun.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.symm.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3 (Localization.algEquiv.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M) x y)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHomClass.linearMapClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))))))) (AlgEquiv.symm.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.isLocalization.{u2} R _inst_1 M) x y)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (SMulZeroClass.toSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toZero.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toAddZeroClass.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHomClass.linearMapClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))))))) (AlgEquiv.symm.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.isLocalization.{u2} R _inst_1 M) x y)
 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_symm_mk' Localization.algEquiv_symm_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) :
@@ -1718,7 +1718,7 @@ theorem algEquiv_symm_mk' (x : R) (y : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgEquiv.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) => (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) -> S) (AlgEquiv.hasCoeToFun.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (Localization.algEquiv.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x y)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R (CommMonoid.toMonoid.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R (CommMonoid.toMonoid.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R (CommMonoid.toMonoid.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1))))) x M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (fun (_x : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (SMulZeroClass.toSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toZero.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toAddZeroClass.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u2, u2, u1, max u2 u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (AlgHomClass.linearMapClass.{u2, u2, u1, max u2 u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3)))))) (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M x y)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R (CommMonoid.toMonoid.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R (CommMonoid.toMonoid.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R (CommMonoid.toMonoid.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1))))) x M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (fun (_x : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (SMulZeroClass.toSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toZero.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R 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 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_mk Localization.algEquiv_mkₓ'. -/
 theorem algEquiv_mk (x y) : algEquiv M S (mk x y) = mk' S x y := by rw [mk_eq_mk', alg_equiv_mk']
 #align localization.alg_equiv_mk Localization.algEquiv_mk
@@ -1727,7 +1727,7 @@ theorem algEquiv_mk (x y) : algEquiv M S (mk x y) = mk' S x y := by rw [mk_eq_mk
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgEquiv.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgEquiv.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) => S -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (AlgEquiv.hasCoeToFun.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.symm.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3 (Localization.algEquiv.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x y)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 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R _inst_1)) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))))))) (AlgEquiv.symm.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M x y)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (SMulZeroClass.toSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toZero.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toAddZeroClass.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 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(CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) 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u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHomClass.linearMapClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))))))) (AlgEquiv.symm.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (Localization.mk.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M x y)
 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_symm_mk Localization.algEquiv_symm_mkₓ'. -/
 theorem algEquiv_symm_mk (x : R) (y : M) : (algEquiv M S).symm (mk' S x y) = mk x y := by
   rw [mk_eq_mk', alg_equiv_symm_mk']

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -1593,7 +1593,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))}, Eq.{succ u1} (Submonoid.LocalizationMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toCommMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M))) (IsLocalization.toLocalizationMap.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M)) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))}, Eq.{succ u1} (Submonoid.LocalizationMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toCommMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (IsLocalization.toLocalizationMap.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.instIsLocalizationLocalizationToCommMonoidInstCommSemiringLocalizationToCommMonoidInstAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoidId.{u1} R _inst_1 M)) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))}, Eq.{succ u1} (Submonoid.LocalizationMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toCommMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (IsLocalization.toLocalizationMap.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M)) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)
 Case conversion may be inaccurate. Consider using '#align localization.to_localization_map_eq_monoid_of Localization.toLocalizationMap_eq_monoidOfₓ'. -/
 @[simp]
 theorem toLocalizationMap_eq_monoidOf : toLocalizationMap M (Localization M) = monoidOf M :=
@@ -1624,7 +1624,7 @@ theorem mk_one_eq_algebraMap (x) : mk x 1 = algebraMap R (Localization M) x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R) (y : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x y) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M) x y)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R) (y : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x y) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.instIsLocalizationLocalizationToCommMonoidInstCommSemiringLocalizationToCommMonoidInstAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoidId.{u1} R _inst_1 M) x y)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R) (y : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x y) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M) x y)
 Case conversion may be inaccurate. Consider using '#align localization.mk_eq_mk'_apply Localization.mk_eq_mk'_applyₓ'. -/
 theorem mk_eq_mk'_apply (x y) : mk x y = IsLocalization.mk' (Localization M) x y := by
   rw [mk_eq_monoid_of_mk'_apply, mk', to_localization_map_eq_monoid_of]
@@ -1634,7 +1634,7 @@ theorem mk_eq_mk'_apply (x y) : mk x y = IsLocalization.mk' (Localization M) x y
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))}, Eq.{succ u1} (R -> (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))}, Eq.{succ u1} (R -> (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.instIsLocalizationLocalizationToCommMonoidInstCommSemiringLocalizationToCommMonoidInstAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoidId.{u1} R _inst_1 M))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))}, Eq.{succ u1} (R -> (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M))
 Case conversion may be inaccurate. Consider using '#align localization.mk_eq_mk' Localization.mk_eq_mk'ₓ'. -/
 @[simp]
 theorem mk_eq_mk' : (mk : R → M → Localization M) = IsLocalization.mk' (Localization M) :=
@@ -1695,7 +1695,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgEquiv.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) => (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) -> S) (AlgEquiv.hasCoeToFun.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (Localization.algEquiv.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M) x y)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.instIsLocalizationLocalizationToCommMonoidInstCommSemiringLocalizationToCommMonoidInstAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoidId.{u2} R _inst_1 M) x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (fun (_x : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) 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(Algebra.id.{u2} R _inst_1))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (AlgHomClass.linearMapClass.{u2, u2, u1, max u2 u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3)))))) (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.instIsLocalizationLocalizationToCommMonoidInstCommSemiringLocalizationToCommMonoidInstAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoidId.{u2} R _inst_1 M) x y)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.isLocalization.{u2} R _inst_1 M) x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (fun (_x : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) => S) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u2, u2, u1, max u2 u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (AlgHomClass.linearMapClass.{u2, u2, u1, max u2 u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u2, u1} (AlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3) R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3)))))) (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.isLocalization.{u2} R _inst_1 M) x y)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_mk' Localization.algEquiv_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) = mk' S x y :=
@@ -1706,7 +1706,7 @@ theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgEquiv.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgEquiv.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) => S -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (AlgEquiv.hasCoeToFun.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.symm.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3 (Localization.algEquiv.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u1, u1} R _inst_1 M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) (Localization.isLocalization.{u1} R _inst_1 M) x y)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (SMulZeroClass.toSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toZero.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toAddZeroClass.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) 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(CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) 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R _inst_1)) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))))))) (AlgEquiv.symm.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.instIsLocalizationLocalizationToCommMonoidInstCommSemiringLocalizationToCommMonoidInstAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoidId.{u2} R _inst_1 M) x y)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (SMulZeroClass.toSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toZero.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toAddZeroClass.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 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(CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) 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u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHomClass.linearMapClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))))))) (AlgEquiv.symm.{u2, u2, u1} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (CommSemiring.toSemiring.{u1} S _inst_2) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) _inst_3 (Localization.algEquiv.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u2, u2} R _inst_1 M (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (Localization.isLocalization.{u2} R _inst_1 M) x y)
 Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_symm_mk' Localization.algEquiv_symm_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) :

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

@@ -129,7 +129,7 @@ variable (M)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M N) -> (forall (r : 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.hasMem.{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)))))) r N) -> (IsUnit.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r))) -> (IsLocalization.{u1, u2} R _inst_1 N S _inst_2 _inst_3)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))), (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M N) -> (forall (r : 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)))))) r N) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) r))) -> (IsLocalization.{u2, u1} R _inst_1 N S _inst_2 _inst_3)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))), (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M N) -> (forall (r : 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)))))) r N) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) r))) -> (IsLocalization.{u2, u1} R _inst_1 N S _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align is_localization.of_le IsLocalization.of_leₓ'. -/
 theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (algebraMap R S r)) :
     IsLocalization N S :=
@@ -184,7 +184,7 @@ theorem toLocalizationMap_toMap : (toLocalizationMap M S).toMap = (algebraMap R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} S (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) (fun (_x : MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) (Submonoid.LocalizationMap.toMap.{u1, u2} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M S (CommSemiring.toCommMonoid.{u2} S _inst_2) (IsLocalization.toLocalizationMap.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R S (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))))) (Submonoid.LocalizationMap.toMap.{u1, u2} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M S (CommSemiring.toCommMonoid.{u2} S _inst_2) (IsLocalization.toLocalizationMap.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R S (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))))) (Submonoid.LocalizationMap.toMap.{u1, u2} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M S (CommSemiring.toCommMonoid.{u2} S _inst_2) (IsLocalization.toLocalizationMap.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.to_localization_map_to_map_apply IsLocalization.toLocalizationMap_toMap_applyₓ'. -/
 theorem toLocalizationMap_toMap_apply (x) : (toLocalizationMap M S).toMap x = algebraMap R S x :=
   rfl
@@ -221,7 +221,7 @@ theorem toLocalizationMap_sec : (toLocalizationMap M S).sec = sec M :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) (Prod.snd.{u1, u1} R (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)))))) M) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (Prod.fst.{u1, u1} R (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)))))) M) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))
 but is expected to have type
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(RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_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))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (Prod.fst.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (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))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) z (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_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))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (Prod.fst.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_spec IsLocalization.sec_specₓ'. -/
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x` (so this lemma is true by definition). -/
@@ -234,7 +234,7 @@ theorem sec_spec (z : S) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (Prod.fst.{u1, u1} R (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)))))) M) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) (Prod.snd.{u1, u1} R (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)))))) M) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) z)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Prod.fst.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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_inst_5 z)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (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))))) M)) (Prod.snd.{u1, u1} R (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 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_inst_1))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) _inst_2))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_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))))) M)) (Prod.snd.{u1, u1} R (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 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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Prod.fst.{u1, u1} R (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 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_inst_1))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) _inst_2))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) z)
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_spec' IsLocalization.sec_spec'ₓ'. -/
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x`, so this lemma is just an application of `S`'s commutativity. -/
@@ -249,7 +249,7 @@ variable {R M}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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} 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((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 (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 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_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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) c) y))) -> (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} 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(CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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 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(fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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 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(CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c) y))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_right_cancel IsLocalization.map_right_cancelₓ'. -/
 theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap R S (c * y)) :
     algebraMap R S x = algebraMap R S y :=
@@ -260,7 +260,7 @@ theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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} 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_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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) c)))) -> (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R 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 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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 M)}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c))) (FunLike.coe.{max (succ u2) (succ u1), succ 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_inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) y (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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 M)}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c))) (FunLike.coe.{max (succ u2) (succ u1), succ 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_inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) y (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_left_cancel IsLocalization.map_left_cancelₓ'. -/
 theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R S (y * c)) :
     algebraMap R S x = algebraMap R S y :=
@@ -271,7 +271,7 @@ theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {z : S} {x : R} {y : 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)))))) M}, (Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{succ u2} S z (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {z : S} {x : R} {y : 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 M)}, (Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) -> (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} S z (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2)))))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {z : S} {x : R} {y : 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 M)}, (Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) -> (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} S z (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align is_localization.eq_zero_of_fst_eq_zero IsLocalization.eq_zero_of_fst_eq_zeroₓ'. -/
 theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebraMap R S x)
     (hx : x = 0) : z = 0 := by
@@ -285,7 +285,7 @@ variable (M S)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (r : R), Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (Exists.{succ u1} (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)))))) M) (fun (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)))))) M) => Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) m) r) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (r : R), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))))) (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 _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 M)) (fun (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 M)) => Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (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))))) M)) m) r) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (r : R), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))))) (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 _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 M)) (fun (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 M)) => Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (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))))) M)) m) r) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_eq_zero_iff IsLocalization.map_eq_zero_iffₓ'. -/
 theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r = 0 :=
   by
@@ -333,7 +333,7 @@ theorem mk'_mul (x₁ x₂ : R) (y₁ y₂ : M) : mk' S (x₁ * x₂) (y₁ * y
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (OfNat.ofNat.{u1} (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)))))) M) 1 (OfNat.mk.{u1} (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)))))) M) 1 (One.one.{u1} (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)))))) M) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (OfNat.ofNat.{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 _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 M)) 1 (One.toOfNat1.{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 _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 M)) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (OfNat.ofNat.{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 _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 M)) 1 (One.toOfNat1.{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 _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 M)) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_one IsLocalization.mk'_oneₓ'. -/
 theorem mk'_one (x) : mk' S x (1 : M) = algebraMap R S x :=
   (toLocalizationMap M S).mk'_one _
@@ -343,7 +343,7 @@ theorem mk'_one (x) : mk' S x (1 : M) = algebraMap R S x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec IsLocalization.mk'_specₓ'. -/
 @[simp]
 theorem mk'_spec (x) (y : M) : mk' S x y * algebraMap R S y = algebraMap R S x :=
@@ -354,7 +354,7 @@ theorem mk'_spec (x) (y : M) : mk' S x y * algebraMap R S y = algebraMap R S x :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) M)) y)) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec' IsLocalization.mk'_spec'ₓ'. -/
 @[simp]
 theorem mk'_spec' (x) (y : M) : algebraMap R S y * mk' S x y = algebraMap R S x :=
@@ -365,7 +365,7 @@ theorem mk'_spec' (x) (y : M) : algebraMap R S y * mk' S x y = algebraMap R S x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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.hasMem.{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)))))) y M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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.hasMem.{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)))))) x M) y hy)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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)))))) y M), Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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 M) y hy)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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)))))) y M), Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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 M) y hy)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec_mk IsLocalization.mk'_spec_mkₓ'. -/
 @[simp]
 theorem mk'_spec_mk (x) (y : R) (hy : y ∈ M) :
@@ -377,7 +377,7 @@ theorem mk'_spec_mk (x) (y : R) (hy : y ∈ M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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.hasMem.{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)))))) y M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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.hasMem.{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)))))) x M) y hy))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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)))))) y M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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 M) y hy))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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)))))) y M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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 M) y hy))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec'_mk IsLocalization.mk'_spec'_mkₓ'. -/
 @[simp]
 theorem mk'_spec'_mk (x) (y : R) (hy : y ∈ M) :
@@ -391,7 +391,7 @@ variable {S}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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)))))) M} {z : S}, Iff (Eq.{succ u2} S z (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R 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R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 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(NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {z : S}, Iff (Eq.{succ u1} S z (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x))
 Case conversion may be inaccurate. Consider using '#align is_localization.eq_mk'_iff_mul_eq IsLocalization.eq_mk'_iff_mul_eqₓ'. -/
 theorem eq_mk'_iff_mul_eq {x} {y : M} {z} :
     z = mk' S x y ↔ z * algebraMap R S y = algebraMap R S x :=
@@ -402,7 +402,7 @@ theorem eq_mk'_iff_mul_eq {x} {y : M} {z} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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)))))) M} {z : S}, Iff (Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, 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(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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {z : S}, Iff (Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {z : S}, Iff (Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq_mul IsLocalization.mk'_eq_iff_eq_mulₓ'. -/
 theorem mk'_eq_iff_eq_mul {x} {y : M} {z} :
     mk' S x y = z ↔ algebraMap R S x = z * algebraMap R S y :=
@@ -413,7 +413,7 @@ theorem mk'_eq_iff_eq_mul {x} {y : M} {z} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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)))))) M} {z₁ : S} {z₂ : S}, Iff (Eq.{succ u2} S (HAdd.hAdd.{u2, u2, u2} S S S (instHAdd.{u2} S (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z₁) z₂) (Eq.{succ u2} S (HAdd.hAdd.{u2, u2, u2} S S S (instHAdd.{u2} S (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z₁ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S 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(Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x M))))) y))))
 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)))) (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => 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(MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {z₁ : S} {z₂ : S}, Iff (Eq.{succ u1} S (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z₁) z₂) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R 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R _inst_1))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z₁ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S 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(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))))) M)) y))))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_add_eq_iff_add_mul_eq_mul IsLocalization.mk'_add_eq_iff_add_mul_eq_mulₓ'. -/
 theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
     mk' S x y + z₁ = z₂ ↔ algebraMap R S x + z₁ * algebraMap R S y = z₂ * algebraMap R S y := by
@@ -465,7 +465,7 @@ def uniqueOfZeroMem (h : (0 : R) ∈ M) : Unique S :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x₁ : R} {x₂ : R} {y₁ : 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)))))) M} {y₂ : 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)))))) M}, Iff (Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₁ y₁) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₂ y₂)) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) 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 but is expected to have type
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(MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₁) x₂)))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x₁ : R} {x₂ : R} {y₁ : 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 M)} {y₂ : 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 M)}, Iff (Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₁ y₁) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₂ y₂)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₂) x₁)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₂) x₁)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₁) x₂)))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq IsLocalization.mk'_eq_iff_eqₓ'. -/
 theorem mk'_eq_iff_eq {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (y₂ * x₁) = algebraMap R S (y₁ * x₂) :=
@@ -476,7 +476,7 @@ theorem mk'_eq_iff_eq {x₁ x₂} {y₁ y₂ : M} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x₁ : R} {x₂ : R} {y₁ : 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)))))) M} {y₂ : 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)))))) M}, Iff (Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₁ y₁) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₂ y₂)) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) 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 but is expected to have type
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(MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S 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(Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₁))))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x₁ : R} {x₂ : R} {y₁ : 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 M)} {y₂ : 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 M)}, Iff (Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₁ y₁) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₂ y₂)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x₁ (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₂))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x₁ (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₂))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x₂ (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₁))))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq' IsLocalization.mk'_eq_iff_eq'ₓ'. -/
 theorem mk'_eq_iff_eq' {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (x₁ * y₂) = algebraMap R S (x₂ * y₁) :=
@@ -487,7 +487,7 @@ theorem mk'_eq_iff_eq' {x₁ x₂} {y₁ y₂ : M} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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)))))) M} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)}, Iff (Membership.Mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) I) (Membership.Mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) I)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)}, Iff (Membership.mem.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) I) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) I)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)}, Iff (Membership.mem.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) I) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) I)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iffₓ'. -/
 theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R S x ∈ I :=
   by
@@ -552,7 +552,7 @@ variable [Algebra R P] [IsLocalization M P]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R P _inst_1 (CommSemiring.toSemiring.{u3} P _inst_4)] [_inst_7 : IsLocalization.{u1, u3} R _inst_1 M P _inst_4 _inst_6] {x : R} {y : R}, Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y)) (Eq.{succ u3} P (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (algebraMap.{u1, u3} R P _inst_1 (CommSemiring.toSemiring.{u3} P _inst_4) _inst_6) x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (algebraMap.{u1, u3} R P _inst_1 (CommSemiring.toSemiring.{u3} P _inst_4) _inst_6) y))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u2, u3} R _inst_1 M S _inst_2 _inst_3] [_inst_6 : Algebra.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4)] [_inst_7 : IsLocalization.{u2, u1} R _inst_1 M P _inst_4 _inst_6] {x : R} {y : R}, Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) y)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) (algebraMap.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4) _inst_6) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) (algebraMap.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4) _inst_6) y))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u2, u3} R _inst_1 M S _inst_2 _inst_3] [_inst_6 : Algebra.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4)] [_inst_7 : IsLocalization.{u2, u1} R _inst_1 M P _inst_4 _inst_6] {x : R} {y : R}, Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) y)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) (algebraMap.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4) _inst_6) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) (algebraMap.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4) _inst_6) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.eq_iff_eq IsLocalization.eq_iff_eqₓ'. -/
 theorem eq_iff_eq {x y} :
     algebraMap R S x = algebraMap R S y ↔ algebraMap R P x = algebraMap R P y :=
@@ -632,7 +632,7 @@ end Ext
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (z : 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)))))) M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 y z)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y) z)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (z : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 y z)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x y) z)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (z : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 y z)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x y) z)
 Case conversion may be inaccurate. Consider using '#align is_localization.mul_mk'_eq_mk'_of_mul IsLocalization.mul_mk'_eq_mk'_of_mulₓ'. -/
 theorem mul_mk'_eq_mk'_of_mul (x y : R) (z : M) :
     (algebraMap R S) x * mk' S y z = mk' S (x * y) z :=
@@ -643,7 +643,7 @@ theorem mul_mk'_eq_mk'_of_mul (x y : R) (z : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) y))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) y))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_mul_mk'_one IsLocalization.mk'_eq_mul_mk'_oneₓ'. -/
 theorem mk'_eq_mul_mk'_one (x : R) (y : M) : mk' S x y = (algebraMap R S) x * mk' S 1 y :=
   ((toLocalizationMap M S).mul_mk'_one_eq_mk' _ _).symm
@@ -653,7 +653,7 @@ theorem mk'_eq_mul_mk'_one (x : R) (y : M) : mk' S x y = (algebraMap R S) x * mk
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y) x) y) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y) x) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y) x) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_cancel_left IsLocalization.mk'_mul_cancel_leftₓ'. -/
 @[simp]
 theorem mk'_mul_cancel_left (x : R) (y : M) : mk' S (y * x : R) y = (algebraMap R S) x :=
@@ -664,7 +664,7 @@ theorem mk'_mul_cancel_left (x : R) (y : M) : mk' S (y * x : R) y = (algebraMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y)) y) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_cancel_right IsLocalization.mk'_mul_cancel_rightₓ'. -/
 theorem mk'_mul_cancel_right (x : R) (y : M) : mk' S (x * y) y = (algebraMap R S) x :=
   (toLocalizationMap M S).mk'_mul_cancel_right _ _
@@ -699,7 +699,7 @@ variable (M)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHom.comp.{u1, u2, u3} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] (j : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (RingHom.comp.{u1, u3, u2} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) j (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _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))))) M)) y))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] (j : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (RingHom.comp.{u1, u3, u2} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) j (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _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))))) M)) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.is_unit_comp IsLocalization.isUnit_compₓ'. -/
 theorem isUnit_comp (j : S →+* P) (y : M) : IsUnit (j.comp (algebraMap R S) y) :=
   (toLocalizationMap M S).isUnit_comp j.toMonoidHom _
@@ -711,7 +711,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g y)))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))}, (forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))) -> (forall {x : R} {y : R}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) 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 _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u3, u1} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) 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 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 Case conversion may be inaccurate. Consider using '#align is_localization.eq_of_eq IsLocalization.eq_of_eqₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g(M) ⊆ units P`, `f x = f y → g x = g y` for all `x y : R`. -/
@@ -742,7 +742,7 @@ theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (h : forall (y : 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 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 but is expected to have type
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R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) z₁)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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 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(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))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R 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(SetLike.coe.{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))))) M)) y)) z₂))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] {g : RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} (h : forall (y : 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 M)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} 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_inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) z₂))
 Case conversion may be inaccurate. Consider using '#align is_localization.mul_add_inv_left IsLocalization.mul_add_inv_leftₓ'. -/
 theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (w z₁ z₂ : P) :
     w * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) h y)⁻¹ + z₁ = z₂ ↔ w + g y * z₁ = g y * z₂ :=
@@ -757,7 +757,7 @@ theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (
 lean 3 declaration is
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(coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M))))) (Prod.snd.{u1, u1} R (coeSort.{succ u1, 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 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _inst_1))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R 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(Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (NonUnitalNonAssocSemiring.toDistrib.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) _inst_4)))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) 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_inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) w')) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) v))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))) (z : S) (w : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (w' : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (v : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (HAdd.hAdd.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (instHAdd.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (Distrib.toAdd.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (NonUnitalNonAssocSemiring.toDistrib.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) _inst_4)))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) z) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S P (MulOneClass.toMul.{u1} S (MulZeroOneClass.toMulOneClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))))) (MulOneClass.toMul.{u2} P (MulZeroOneClass.toMulOneClass.{u2} P (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S P (MulZeroOneClass.toMulOneClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2)))) (MulZeroOneClass.toMulOneClass.{u2} P (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4))))))) (Submonoid.LocalizationWithZeroMap.lift.{u3, u1, u2} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1) M S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2) P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4) (IsLocalization.toLocalizationWithZeroMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) (RingHom.toMonoidWithZeroHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) g) hg) z) w) w') v) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (Prod.fst.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) v))
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_spec_mul_add IsLocalization.lift_spec_mul_addₓ'. -/
 theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w' v) :
     ((toLocalizationWithZeroMap M S).lift g.toMonoidWithZeroHom hg) z * w + w' = v ↔
@@ -773,7 +773,7 @@ theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w'
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) -> (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (y : 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 M)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g (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))))) M)) y))) -> (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (y : 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 M)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g (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))))) M)) y))) -> (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))
 Case conversion may be inaccurate. Consider using '#align is_localization.lift IsLocalization.liftₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
@@ -801,7 +801,7 @@ variable {g : R →+* P} (hg : ∀ y : M, IsUnit (g y))
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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M) hg) y))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _inst_1))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R 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(CommSemiring.toSemiring.{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 _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MulOneClass.toMul.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M))) (MulOneClass.toMul.{u2} (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MonoidHom.monoidHomClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))))) (IsUnit.liftRight.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) P (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M) (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (MonoidHom.restrict.{u3, u2, u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) P (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instSubmonoidClassSubmonoidInstSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (RingHom.toMonoidHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) g) M) hg) y))))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} 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(CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MulOneClass.toMul.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Monoid.toMulOneClass.{u3} (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R 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(CommSemiring.toSemiring.{u2} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R 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(SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{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 _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MonoidHom.monoidHomClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))))) (IsUnit.liftRight.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) P (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M) (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (MonoidHom.restrict.{u3, u2, u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) P (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instSubmonoidClassSubmonoidInstSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (RingHom.toMonoidHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) g) M) hg) y))))
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk' IsLocalization.lift_mk'ₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
@@ -815,7 +815,7 @@ theorem lift_mk' (x y) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 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 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} 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(Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P 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(CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) v) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P 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(MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) P ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) v))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} 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 Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk'_spec IsLocalization.lift_mk'_specₓ'. -/
 theorem lift_mk'_spec (x v) (y : M) : lift hg (mk' S x y) = v ↔ g x = g y * v :=
   (toLocalizationMap M S).lift_mk'_spec _ _ _ _
@@ -825,7 +825,7 @@ theorem lift_mk'_spec (x v) (y : M) : lift hg (mk' S x y) = v ↔ g x = g y * v
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) (x : R), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => S -> P) (RingHom.hasCoeToFun.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (IsLocalization.lift.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (MonoidWithZero.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, 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(Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (RingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) P (Semiring.toNonAssocSemiring.{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) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (RingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) P (Semiring.toNonAssocSemiring.{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) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) P (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u1, u3} (RingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) P (Semiring.toNonAssocSemiring.{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) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u1, u3} (RingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) P (Semiring.toNonAssocSemiring.{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) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) P (Semiring.toNonAssocSemiring.{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) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) P (Semiring.toNonAssocSemiring.{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) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) (IsLocalization.lift.{u2, u1, u3} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (MonoidWithZero.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) => P) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} 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 Case conversion may be inaccurate. Consider using '#align is_localization.lift_eq IsLocalization.lift_eqₓ'. -/
 @[simp]
 theorem lift_eq (x : R) : lift hg ((algebraMap R S) x) = g x :=
@@ -836,7 +836,7 @@ theorem lift_eq (x : R) : lift hg ((algebraMap R S) x) = g x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 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R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.hasMem.{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)))))) x M))))) (Prod.snd.{u1, u1} R (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)))))) M) x)))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M))} {y : Prod.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M))}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (Prod.fst.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, 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(NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{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 _inst_1)))))) x M)) x))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (Prod.fst.{u3, u3} R (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 _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 _inst_1))))) R 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(Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g 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(Prod.snd.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) y)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (HMul.hMul.{u3, u3, u3} R R R (instHMul.{u3} R (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Prod.fst.{u3, u3} R (Subtype.{succ u3} R 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(Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) (Prod.snd.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) y)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (HMul.hMul.{u3, u3, u3} R R R (instHMul.{u3} R (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Prod.fst.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) y) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) (Prod.snd.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) x)))))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))) {x : Prod.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M))} {y : Prod.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M))}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (Prod.fst.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, 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(NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{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 _inst_1)))))) x M)) x))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (Prod.fst.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) x) (Prod.snd.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) x))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S P 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(Prod.snd.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) y)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) 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 Case conversion may be inaccurate. Consider using '#align is_localization.lift_eq_iff IsLocalization.lift_eq_iffₓ'. -/
 theorem lift_eq_iff {x y : R × M} :
     lift hg (mk' S x.1 x.2) = lift hg (mk' S y.1 y.2) ↔ g (x.1 * y.2) = g (y.1 * x.2) :=
@@ -847,7 +847,7 @@ theorem lift_eq_iff {x y : R × M} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 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(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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))), Eq.{max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHom.comp.{u1, u2, u3} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (IsLocalization.lift.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) g
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))), Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHom.comp.{u3, u1, u2} R S P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (algebraMap.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) g
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))), Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHom.comp.{u3, u1, u2} R S P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (algebraMap.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) g
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_comp IsLocalization.lift_compₓ'. -/
 @[simp]
 theorem lift_comp : (lift hg).comp (algebraMap R S) = g :=
@@ -909,7 +909,7 @@ theorem algHom_subsingleton [Algebra R P] : Subsingleton (S →ₐ[R] P) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : S -> P) (k : S -> P), (Eq.{succ u3} P (j (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (OfNat.ofNat.{u3} P 1 (OfNat.mk.{u3} P 1 (One.one.{u3} P (AddMonoidWithOne.toOne.{u3} P (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} P (NonAssocSemiring.toAddCommMonoidWithOne.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) -> (Eq.{succ u3} P (k (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (OfNat.ofNat.{u3} P 1 (OfNat.mk.{u3} P 1 (One.one.{u3} P (AddMonoidWithOne.toOne.{u3} P (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} P (NonAssocSemiring.toAddCommMonoidWithOne.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) -> (forall (a : S) (b : S), Eq.{succ u3} P (j (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) (j a) (j b))) -> (forall (a : S) (b : S), Eq.{succ u3} P (k (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) (k a) (k b))) -> (forall (a : R), Eq.{succ u3} P (j (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a)) (k (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a))) -> (Eq.{max (succ u2) (succ u3)} (S -> P) j k)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : S -> P) (k : S -> P), (Eq.{succ u3} P (j (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> (Eq.{succ u3} P (k (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> (forall (a : S) (b : S), Eq.{succ u3} P (j (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (j a) (j b))) -> (forall (a : S) (b : S), Eq.{succ u3} P (k (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (k a) (k b))) -> (forall (a : R), Eq.{succ u3} P (j (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a)) (k (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a))) -> (Eq.{max (succ u2) (succ u3)} (S -> P) j k)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : S -> P) (k : S -> P), (Eq.{succ u3} P (j (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> (Eq.{succ u3} P (k (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> (forall (a : S) (b : S), Eq.{succ u3} P (j (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (j a) (j b))) -> (forall (a : S) (b : S), Eq.{succ u3} P (k (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (k a) (k b))) -> (forall (a : R), Eq.{succ u3} P (j (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a)) (k (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a))) -> (Eq.{max (succ u2) (succ u3)} (S -> P) j k)
 Case conversion may be inaccurate. Consider using '#align is_localization.ext IsLocalization.extₓ'. -/
 /-- To show `j` and `k` agree on the whole localization, it suffices to show they agree
 on the image of the base ring, if they preserve `1` and `*`. -/
@@ -925,7 +925,7 @@ variable {M}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) {j : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (x : R), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => S -> P) (RingHom.hasCoeToFun.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) j (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x)) -> (Eq.{max (succ u2) (succ u3)} (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (IsLocalization.lift.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) j)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) y))) {j : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))}, (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g x)) -> (Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (IsLocalization.lift.{u1, u3, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) j)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) y))) {j : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))}, (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) j (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g x)) -> (Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (IsLocalization.lift.{u1, u3, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) j)
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_unique IsLocalization.lift_uniqueₓ'. -/
 theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) : lift hg = j :=
   RingHom.ext <|
@@ -938,7 +938,7 @@ theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : S), Eq.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (IsLocalization.lift.{u1, u2, u2} R _inst_1 M S _inst_2 _inst_3 S _inst_2 _inst_5 (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (IsLocalization.map_units.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) x
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.lift.{u1, u2, u2} R _inst_1 M S _inst_2 _inst_3 S _inst_2 _inst_5 (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (IsLocalization.map_units.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) x
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.lift.{u1, u2, u2} R _inst_1 M S _inst_2 _inst_3 S _inst_2 _inst_5 (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (IsLocalization.map_units.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) x
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_id IsLocalization.lift_idₓ'. -/
 @[simp]
 theorem lift_id (x) : lift (map_units S : ∀ y : M, IsUnit _) x = x :=
@@ -949,7 +949,7 @@ theorem lift_id (x) : lift (map_units S : ∀ y : M, IsUnit _) x = x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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 but is expected to have type
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(RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) (Prod.snd.{u1, u1} R (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 M)) x)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Prod.fst.{u1, u1} R (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 M)) x))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) y))), Iff (Function.Surjective.{succ u3, succ u2} S P (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S 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P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Prod.fst.{u1, u1} R (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 M)) x))))
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_surjective_iff IsLocalization.lift_surjective_iffₓ'. -/
 theorem lift_surjective_iff :
     Surjective (lift hg : S → P) ↔ ∀ v : P, ∃ x : R × M, v * g x.2 = g x.1 :=
@@ -960,7 +960,7 @@ theorem lift_surjective_iff :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))), Iff (Function.Injective.{succ u2, succ u3} S P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => S -> P) (RingHom.hasCoeToFun.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (IsLocalization.lift.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg))) (forall (x : R) (y : R), Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y)) (Eq.{succ u3} P (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g y)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) y))), Iff (Function.Injective.{succ u3, succ u2} S P (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u1, u3, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg))) (forall (x : R) (y : R), Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) y)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g y)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) (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 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P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g y)))
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_injective_iff IsLocalization.lift_injective_iffₓ'. -/
 theorem lift_injective_iff :
     Injective (lift hg : S → P) ↔ ∀ x y, algebraMap R S x = algebraMap R S y ↔ g x = g y :=
@@ -999,7 +999,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => P -> Q) (RingHom.hasCoeToFun.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => Q) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (algebraMap.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) => Q) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (MulHomClass.toFunLike.{max u3 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((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) Q (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S 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(Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (algebraMap.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_eq IsLocalization.map_eqₓ'. -/
 theorem map_eq (x) : map Q g hy ((algebraMap R S) x) = algebraMap P Q (g x) :=
   lift_eq (fun y => map_units _ ⟨g y, hy y.2⟩) x
@@ -1020,7 +1020,7 @@ theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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 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_inst_1)))))) x M) y) (Subtype.property.{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.hasMem.{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)))))) x M) y))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u4, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u4, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Preorder.toLE.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))))) M (Submonoid.comap.{u4, u1, max u4 u1} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u4, u2, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) _inst_4 T Q _inst_6 _inst_7 _inst_8 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) 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(Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y)) (hy (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y))))
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u4, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u4, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Preorder.toLE.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))))) M (Submonoid.comap.{u4, u1, max u4 u1} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u4, u2, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) _inst_4 T Q _inst_6 _inst_7 _inst_8 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) _inst_4))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) _inst_4))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) _inst_4)))))) x_1 T) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y)) (hy (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y))))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_mk' IsLocalization.map_mk'ₓ'. -/
 theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.2⟩ :=
   @Submonoid.LocalizationMap.map_mk' _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom _
@@ -1031,7 +1031,7 @@ theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toMonoidHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ringHomClass.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M)) (le_refl.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) M)), Eq.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (IsLocalization.map.{u1, u2, u1, u2} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) h) z) z
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u2, u2} R R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toMonoidHomClass.{u2, u2, u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M)) (le_refl.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))) M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (IsLocalization.map.{u2, u1, u2, u1} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) h) z) z
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u2, u2} R R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toMonoidHomClass.{u2, u2, u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M)) (le_refl.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))) M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (IsLocalization.map.{u2, u1, u2, u1} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) h) z) z
 Case conversion may be inaccurate. Consider using '#align is_localization.map_id IsLocalization.map_idₓ'. -/
 @[simp]
 theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
@@ -1043,7 +1043,7 @@ theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))), (forall (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) j (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => P -> Q) (RingHom.hasCoeToFun.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x))) -> (Eq.{max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u4}} [_inst_2 : CommSemiring.{u4} S] [_inst_3 : Algebra.{u2, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u2, u4} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u1, max u2 u1} R P (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))), (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (algebraMap.{u2, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) j (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} 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x)) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q 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(CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))) -> (Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (IsLocalization.map.{u2, u4, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u4}} [_inst_2 : CommSemiring.{u4} S] [_inst_3 : Algebra.{u2, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u2, u4} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u1, max u2 u1} R P (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))), (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S 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S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (algebraMap.{u2, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (algebraMap.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6) _inst_7) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))) -> (Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (IsLocalization.map.{u2, u4, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
 Case conversion may be inaccurate. Consider using '#align is_localization.map_unique IsLocalization.map_uniqueₓ'. -/
 theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algebraMap P Q (g x)) :
     map Q g hy = j :=
@@ -1054,7 +1054,7 @@ theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algeb
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toHasLe.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)), Eq.{max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (RingHom.comp.{u2, u4, u6} S Q W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10)) (IsLocalization.map.{u3, u4, u5, u6} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u2, u5, u6} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u3, u5} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) l g) (fun (x : R) (hx : 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.hasMem.{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)))))) x M) => hl (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (FunLike.hasCoeToFun.{succ (max u1 u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u2} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)), Eq.{max (succ u3) (succ u5)} (RingHom.{u3, u5} S W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHom.comp.{u3, u2, u5} S Q W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (IsLocalization.map.{u4, u2, u6, u5} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u3, u4, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u3, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u2} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)), Eq.{max (succ u3) (succ u5)} (RingHom.{u3, u5} S W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHom.comp.{u3, u2, u5} S Q W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (IsLocalization.map.{u4, u2, u6, u5} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u3, u4, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u3, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx)))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_comp_map IsLocalization.map_comp_mapₓ'. -/
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
@@ -1070,7 +1070,7 @@ theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSe
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toHasLe.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)) (x : S), Eq.{succ u6} W (coeFn.{max (succ u4) (succ u6), max (succ u4) (succ u6)} (RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (fun (_x : RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W 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(IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (coeFn.{max (succ u2) (succ u6), max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (fun (_x : RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) => S -> W) (RingHom.hasCoeToFun.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (IsLocalization.map.{u1, u2, u5, u6} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u3, u5} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) l g) (fun (x : R) (hx : 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.hasMem.{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)))))) x M) => hl (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (FunLike.hasCoeToFun.{succ (max u1 u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u3} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)) (x : S), Eq.{succ u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) => W) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (a : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) a) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u1, u2, u4, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (FunLike.coe.{max (succ u5) (succ u3), succ u3, succ u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) => W) _x) (MulHomClass.toFunLike.{max u5 u3, u3, u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (NonUnitalNonAssocSemiring.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)))) (NonUnitalNonAssocSemiring.toMul.{u5} W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))) (NonUnitalRingHomClass.toMulHomClass.{max u5 u3, u3, u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHomClass.toNonUnitalRingHomClass.{max u5 u3, u3, u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (RingHom.instRingHomClassRingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u4, u3, u6, u5} P _inst_4 T ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u1, u2, u4, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (FunLike.coe.{max (succ u5) (succ u2), succ u2, succ u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => W) _x) (MulHomClass.toFunLike.{max u5 u2, u2, u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u5} W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))) (NonUnitalRingHomClass.toMulHomClass.{max u5 u2, u2, u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHomClass.toNonUnitalRingHomClass.{max u5 u2, u2, u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (RingHom.instRingHomClassRingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u1, u2, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx))) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u3} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)) (x : S), Eq.{succ u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) => W) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (a : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) a) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u1, u2, u4, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (FunLike.coe.{max (succ u5) (succ u3), succ u3, succ u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) => W) _x) (MulHomClass.toFunLike.{max u5 u3, u3, u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) 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W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (RingHom.instRingHomClassRingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u4, u3, u6, u5} P _inst_4 T ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u1, u2, u4, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHomClass.toNonUnitalRingHomClass.{max u5 u2, u2, u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (RingHom.instRingHomClassRingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u1, u2, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx))) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.map_map IsLocalization.map_mapₓ'. -/
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
@@ -1084,7 +1084,7 @@ theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemirin
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (SMul.smul.{u1, u2} R S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3))))) z x)) (SMul.smul.{u3, u4} P Q (SMulZeroClass.toHasSmul.{u3, u4} P Q (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} P Q (MulZeroClass.toHasZero.{u3} P (MulZeroOneClass.toMulZeroClass.{u3} P (MonoidWithZero.toMulZeroOneClass.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} P Q (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (Module.toMulActionWithZero.{u3, u4} P Q (CommSemiring.toSemiring.{u3} P _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (Algebra.toModule.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7))))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g z) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (HSMul.hSMul.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (instHSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (Algebra.toSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_4 (CommSemiring.toSemiring.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6) _inst_7)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g z) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (HSMul.hSMul.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) (instHSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) (Algebra.toSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) _inst_4 (CommSemiring.toSemiring.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) x) _inst_6) _inst_7)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g z) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_smul IsLocalization.map_smulₓ'. -/
 theorem map_smul (x : S) (z : R) : map Q g hy (z • x : S) = g z • map Q g hy x := by
   rw [Algebra.smul_def, Algebra.smul_def, RingHom.map_mul, map_eq]
@@ -1146,7 +1146,7 @@ theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T) (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingEquiv.{u2, u4} S Q (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasMul.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))) (Distrib.toHasAdd.{u4} Q 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 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R 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(NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (RingEquivClass.toMulEquivClass.{max u1 u2, u1, u2} (RingEquiv.{u1, u2} S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Distrib.toAdd.{u2} Q (NonUnitalNonAssocSemiring.toDistrib.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u2} Q (NonUnitalNonAssocSemiring.toDistrib.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))))) (RingEquiv.instRingEquivClassRingEquiv.{u1, u2} S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Distrib.toAdd.{u2} Q (NonUnitalNonAssocSemiring.toDistrib.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))))))) (IsLocalization.ringEquivOfRingEquiv.{u4, u1, u3, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 j H) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))) P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))) (algebraMap.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_7) (FunLike.coe.{max (succ u4) (succ u3), succ u4, 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(Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingEquivClass.toMulEquivClass.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))))) j x))
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R 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(NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (MulEquivClass.toEquivLike.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingEquivClass.toMulEquivClass.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))))) j x))
 Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eqₓ'. -/
 @[simp]
 theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x) :
@@ -1604,7 +1604,7 @@ theorem toLocalizationMap_eq_monoidOf : toLocalizationMap M (Localization M) = m
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (fun (_x : MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) => R -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (MonoidHom.hasCoeToFun.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (Submonoid.LocalizationMap.toMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (fun (_x : RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) => R -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (RingHom.hasCoeToFun.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M))) (MonoidHom.monoidHomClass.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))))) (Submonoid.LocalizationMap.toMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M))) (MonoidHom.monoidHomClass.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))))) (Submonoid.LocalizationMap.toMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align localization.monoid_of_eq_algebra_map Localization.monoidOf_eq_algebraMapₓ'. -/
 theorem monoidOf_eq_algebraMap (x) : (monoidOf M).toMap x = algebraMap R (Localization M) x :=
   rfl
@@ -1614,7 +1614,7 @@ theorem monoidOf_eq_algebraMap (x) : (monoidOf M).toMap x = algebraMap R (Locali
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (fun (_x : RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) => R -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (RingHom.hasCoeToFun.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align localization.mk_one_eq_algebra_map Localization.mk_one_eq_algebraMapₓ'. -/
 theorem mk_one_eq_algebraMap (x) : mk x 1 = algebraMap R (Localization M) x :=
   rfl
@@ -1645,7 +1645,7 @@ theorem mk_eq_mk' : (mk : R → M → Localization M) = IsLocalization.mk' (Loca
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : 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_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1)] (m : A), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => A -> R) (RingHom.hasCoeToFun.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (algebraMap.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6) m) (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M))))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (fun (_x : RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) => A -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (RingHom.hasCoeToFun.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (algebraMap.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_5 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (Localization.algebra.{u1, u2} R _inst_1 M A _inst_5 _inst_6)) m)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : 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_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1)] (m : A), Eq.{succ u1} (Localization.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1) M) (Localization.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1) M (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (algebraMap.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6) m) (OfNat.ofNat.{u1} (Subtype.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (fun (x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (fun (x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1))))) x M)) (Submonoid.one.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_5 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u2} R _inst_1 M A _inst_5 _inst_6)) m)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : 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_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1)] (m : A), Eq.{succ u1} (Localization.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) _inst_1) M) (Localization.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) _inst_1) M (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (algebraMap.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6) m) (OfNat.ofNat.{u1} (Subtype.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (fun (x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (fun (x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) _inst_1))))) x M)) (Submonoid.one.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => R) m) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_5 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u2} R _inst_1 M A _inst_5 _inst_6)) m)
 Case conversion may be inaccurate. Consider using '#align localization.mk_algebra_map Localization.mk_algebraMapₓ'. -/
 theorem mk_algebraMap {A : Type _} [CommSemiring A] [Algebra A R] (m : A) :
     mk (algebraMap A R m) 1 = algebraMap A (Localization M) m := by
@@ -1834,7 +1834,7 @@ variable {R M} (S) {K : Type _} [IsLocalization M S]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {x : R}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] {x : R}, (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))) (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] {x : R}, (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))) (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iffₓ'. -/
 theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R S x = 0 ↔ x = 0 :=
   by
@@ -1850,7 +1850,7 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Function.Injective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Function.Injective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align is_localization.injective IsLocalization.injectiveₓ'. -/
 protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraMap R S) :=
   by
@@ -1863,7 +1863,7 @@ protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraM
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {x : R}, (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall {x : R}, (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall {x : R}, (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.to_map_ne_zero_of_mem_non_zero_divisors IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisorsₓ'. -/
 protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M ≤ nonZeroDivisors R)
     {x : R} (hx : x ∈ nonZeroDivisors R) : algebraMap R S x ≠ 0 :=
@@ -1906,7 +1906,7 @@ variable (S M) (Q : Type _) [CommRing Q] {g : R →+* P} [Algebra P Q]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] (Q : Type.{u4}) [_inst_6 : CommRing.{u4} Q] {g : RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u4} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (Ring.toSemiring.{u4} Q (CommRing.toRing.{u4} Q _inst_6))], (Function.Injective.{succ u1, succ u3} R P (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (fun (_x : RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u4} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7], Function.Injective.{succ u2, succ u4} S Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (IsLocalization.map.{u1, u2, u3, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] (Q : Type.{u2}) [_inst_6 : CommRing.{u2} Q] {g : RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u2} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))], (Function.Injective.{succ u4, succ u3} R P (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (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} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u2} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7], Function.Injective.{succ u1, succ u2} S Q (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))) (RingHom.instRingHomClassRingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))))) (IsLocalization.map.{u4, u1, u3, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{max u4 u3, u3, u4} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] (Q : Type.{u2}) [_inst_6 : CommRing.{u2} Q] {g : RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u2} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))], (Function.Injective.{succ u4, succ u3} R P (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (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} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u2} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7], Function.Injective.{succ u1, succ u2} S Q (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Q) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))) (RingHom.instRingHomClassRingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))))) (IsLocalization.map.{u4, u1, u3, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{max u4 u3, u3, u4} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injectiveₓ'. -/
 /-- Injectivity of a map descends to the map induced on localizations. -/
 theorem map_injective_of_injective (hg : Function.Injective g)
@@ -2000,7 +2000,7 @@ open IsLocalization
 lean 3 declaration is
   forall {R : Type.{u1}} {Rₘ : Type.{u2}} [_inst_5 : CommRing.{u1} R] [_inst_6 : CommRing.{u2} Rₘ] {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_5)))))}, (Not (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_5)))))) (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_5)))))) 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_5))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))))) M)) -> (IsField.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) -> (forall [_inst_7 : Algebra.{u1, u2} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u1, succ u2} R Rₘ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) (fun (_x : RingHom.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) => R -> Rₘ) (RingHom.hasCoeToFun.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) (algebraMap.{u1, u2} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)) _inst_7)))
 but is expected to have type
-  forall {R : Type.{u2}} {Rₘ : Type.{u1}} [_inst_5 : CommRing.{u2} R] [_inst_6 : CommRing.{u1} Rₘ] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))}, (Not (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_5)))))) (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_5)))))) 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_5))))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) M)) -> (IsField.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) -> (forall [_inst_7 : Algebra.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} R Rₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Rₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R Rₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))))))) (algebraMap.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)) _inst_7)))
+  forall {R : Type.{u2}} {Rₘ : Type.{u1}} [_inst_5 : CommRing.{u2} R] [_inst_6 : CommRing.{u1} Rₘ] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))}, (Not (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_5)))))) (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_5)))))) 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_5))))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) M)) -> (IsField.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) -> (forall [_inst_7 : Algebra.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} R Rₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Rₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R Rₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))))))) (algebraMap.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align is_field.localization_map_bijective IsField.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommRing Rₘ]
@@ -2019,7 +2019,7 @@ theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommR
 lean 3 declaration is
   forall {K : Type.{u1}} {Kₘ : Type.{u2}} [_inst_5 : Field.{u1} K] [_inst_6 : CommRing.{u2} Kₘ] {M : Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))}, (Not (Membership.Mem.{u1, u1} K (Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))) K (Submonoid.setLike.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))))))) M)) -> (forall [_inst_7 : Algebra.{u1, u2} K Kₘ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u1, u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u2} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u1, succ u2} K Kₘ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) (fun (_x : RingHom.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) => K -> Kₘ) (RingHom.hasCoeToFun.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) (algebraMap.{u1, u2} K Kₘ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)) _inst_7)))
 but is expected to have type
-  forall {K : Type.{u2}} {Kₘ : Type.{u1}} [_inst_5 : Field.{u2} K] [_inst_6 : CommRing.{u1} Kₘ] {M : Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))))}, (Not (Membership.mem.{u2, u2} K (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))))) K (Submonoid.instSetLikeSubmonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))))) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) M)) -> (forall [_inst_7 : Algebra.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} K Kₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Kₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K Kₘ (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) (NonUnitalNonAssocSemiring.toMul.{u1} Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))))))) (algebraMap.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)) _inst_7)))
+  forall {K : Type.{u2}} {Kₘ : Type.{u1}} [_inst_5 : Field.{u2} K] [_inst_6 : CommRing.{u1} Kₘ] {M : Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))))}, (Not (Membership.mem.{u2, u2} K (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))))) K (Submonoid.instSetLikeSubmonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))))) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) M)) -> (forall [_inst_7 : Algebra.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} K Kₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Kₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K Kₘ (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) (NonUnitalNonAssocSemiring.toMul.{u1} Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))))))) (algebraMap.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align field.localization_map_bijective Field.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem Field.localization_map_bijective {K Kₘ : Type _} [Field K] [CommRing Kₘ] {M : Submonoid K}
@@ -2074,7 +2074,7 @@ include S
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Sₘ : Type.{u3}) [_inst_6 : CommRing.{u3} Sₘ] [_inst_9 : Algebra.{u2, u3} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u3} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u1, u2, u3} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} S Sₘ (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u3} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (Algebra.toModule.{u2, u3} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u3} R Sₘ (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Sₘ (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.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u3} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (Algebra.toModule.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)))))] (y : 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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Sₘ _inst_6)))) => R -> Sₘ) (RingHom.hasCoeToFun.{u1, u3} R Sₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) (algebraMap.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12) ((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 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(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))))))) M) 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 M))))) y))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] (Sₘ : Type.{u1}) [_inst_6 : CommRing.{u1} Sₘ] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u2, u3, u1} R S Sₘ (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) (Algebra.toSMul.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_12)] (y : 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 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(NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) M)) y)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_12) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] (Sₘ : Type.{u1}) [_inst_6 : CommRing.{u1} Sₘ] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u2, u3, u1} R S Sₘ (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) (Algebra.toSMul.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_12)] (y : 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 M)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_12) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoidₓ'. -/
 theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R Sₘ y) :=
   by
@@ -2086,7 +2086,7 @@ theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R S
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : R) (y : 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))))))) M) 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))))))) M) 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))))))) M) 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 M))))) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M y)))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u4, u2, u3} R Rₘ Sₘ (Algebra.toSMul.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u4, u1, u3} R S Sₘ (Algebra.toSMul.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] (x : R) (y : 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 M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))))))) (algebraMap.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u1, u3} ((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_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2))))))) x_1 (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (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)))))) M)) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u4} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M y)))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u4, u2, u3} R Rₘ Sₘ (Algebra.toSMul.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u4, u1, u3} R S Sₘ (Algebra.toSMul.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] (x : R) (y : 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 M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))))))) (algebraMap.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u1, u3} ((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_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2))))))) x_1 (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (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)))))) M)) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u4} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M y)))
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_mk' IsLocalization.algebraMap_mk'ₓ'. -/
 @[simp]
 theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
@@ -2129,7 +2129,7 @@ theorem IsLocalization.algebraMap_eq_map_map_submonoid :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : Rₘ), Eq.{succ u4} Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u4} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u3, u4} R Rₘ Sₘ (Algebra.toSMul.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u4} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] (x : Rₘ), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (IsLocalization.map.{u2, u3, u1, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3))])) x)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u4} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u3, u4} R Rₘ Sₘ (Algebra.toSMul.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u4} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] (x : Rₘ), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (IsLocalization.map.{u2, u3, u1, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3))])) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
@@ -2168,7 +2168,7 @@ variable (Rₘ Sₘ)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u3, succ u4} Rₘ Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) (localizationAlgebra.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : 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)))))} {S : Type.{u3}} [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u1}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u1} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u4, succ u3} R S (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (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} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))))))) (algebraMap.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u2, succ u1} Rₘ Sₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) (localizationAlgebra.{u4, u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : 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)))))} {S : Type.{u3}} [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u1}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u1} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u4, succ u3} R S (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (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} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))))))) (algebraMap.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u2, succ u1} Rₘ Sₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) (localizationAlgebra.{u4, u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
 Case conversion may be inaccurate. Consider using '#align localization_algebra_injective localizationAlgebra_injectiveₓ'. -/
 /-- Injectivity of the underlying `algebra_map` descends to the algebra induced by localization. -/
 theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)) :

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

@@ -127,7 +127,7 @@ variable (M)
 
 /- warning: is_localization.of_le -> IsLocalization.of_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M N) -> (forall (r : 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.hasMem.{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)))))) r N) -> (IsUnit.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r))) -> (IsLocalization.{u1, u2} R _inst_1 N S _inst_2 _inst_3)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M N) -> (forall (r : 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.hasMem.{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)))))) r N) -> (IsUnit.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r))) -> (IsLocalization.{u1, u2} R _inst_1 N S _inst_2 _inst_3)
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))), (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M N) -> (forall (r : 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)))))) r N) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) r))) -> (IsLocalization.{u2, u1} R _inst_1 N S _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align is_localization.of_le IsLocalization.of_leₓ'. -/
@@ -979,7 +979,7 @@ variable (Q)
 
 /- warning: is_localization.map -> IsLocalization.map is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} (Q : Type.{u4}) [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) -> (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} (Q : Type.{u4}) [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) -> (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} (Q : Type.{u4}) [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) -> (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))
 Case conversion may be inaccurate. Consider using '#align is_localization.map IsLocalization.mapₓ'. -/
@@ -997,7 +997,7 @@ end
 
 /- warning: is_localization.map_eq -> IsLocalization.map_eq is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => P -> Q) (RingHom.hasCoeToFun.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => P -> Q) (RingHom.hasCoeToFun.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x))
 but is expected to have type
   forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => Q) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u3 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (algebraMap.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_eq IsLocalization.map_eqₓ'. -/
@@ -1007,7 +1007,7 @@ theorem map_eq (x) : map Q g hy ((algebraMap R S) x) = algebraMap P Q (g x) :=
 
 /- warning: is_localization.map_comp -> IsLocalization.map_comp is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7], Eq.{max (succ u1) (succ u4)} (RingHom.{u1, u4} R Q (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHom.comp.{u1, u2, u4} R S Q (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) (RingHom.comp.{u1, u3, u4} R P Q (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) g)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7], Eq.{max (succ u1) (succ u4)} (RingHom.{u1, u4} R Q (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHom.comp.{u1, u2, u4} R S Q (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) (RingHom.comp.{u1, u3, u4} R P Q (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) g)
 but is expected to have type
   forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u4, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u4, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Preorder.toLE.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))))) M (Submonoid.comap.{u4, u1, max u4 u1} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} R Q (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHom.comp.{u4, u2, u3} R S Q (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (IsLocalization.map.{u4, u2, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (algebraMap.{u4, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) (RingHom.comp.{u4, u1, u3} R P Q (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (algebraMap.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6) _inst_7) g)
 Case conversion may be inaccurate. Consider using '#align is_localization.map_comp IsLocalization.map_compₓ'. -/
@@ -1018,7 +1018,7 @@ theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g
 
 /- warning: is_localization.map_mk' -> IsLocalization.map_mk' is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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 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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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_inst_1)))))) x M) y) (Subtype.property.{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.hasMem.{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)))))) x M) y))))
 but is expected to have type
   forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u4, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u4, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Preorder.toLE.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))))) M (Submonoid.comap.{u4, u1, max u4 u1} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u4, u2, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) _inst_4 T Q _inst_6 _inst_7 _inst_8 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) _inst_4))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) _inst_4))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) _inst_4)))))) x_1 T) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y)) (hy (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y))))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_mk' IsLocalization.map_mk'ₓ'. -/
@@ -1029,7 +1029,7 @@ theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.
 
 /- warning: is_localization.map_id -> IsLocalization.map_id is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toMonoidHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ringHomClass.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M)) (le_refl.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) M)), Eq.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (IsLocalization.map.{u1, u2, u1, u2} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) h) z) z
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toMonoidHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ringHomClass.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M)) (le_refl.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) M)), Eq.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (IsLocalization.map.{u1, u2, u1, u2} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) h) z) z
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u2, u2} R R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toMonoidHomClass.{u2, u2, u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M)) (le_refl.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))) M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (IsLocalization.map.{u2, u1, u2, u1} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) h) z) z
 Case conversion may be inaccurate. Consider using '#align is_localization.map_id IsLocalization.map_idₓ'. -/
@@ -1041,7 +1041,7 @@ theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
 
 /- warning: is_localization.map_unique -> IsLocalization.map_unique is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))), (forall (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) j (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => P -> Q) (RingHom.hasCoeToFun.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x))) -> (Eq.{max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))), (forall (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) j (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => P -> Q) (RingHom.hasCoeToFun.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x))) -> (Eq.{max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u4}} [_inst_2 : CommSemiring.{u4} S] [_inst_3 : Algebra.{u2, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u2, u4} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u1, max u2 u1} R P (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))), (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S 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x)) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))) -> (Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (IsLocalization.map.{u2, u4, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
 Case conversion may be inaccurate. Consider using '#align is_localization.map_unique IsLocalization.map_uniqueₓ'. -/
@@ -1052,7 +1052,7 @@ theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algeb
 
 /- warning: is_localization.map_comp_map -> IsLocalization.map_comp_map is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toLE.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)), Eq.{max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (RingHom.comp.{u2, u4, u6} S Q W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10)) (IsLocalization.map.{u3, u4, u5, u6} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u2, u5, u6} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u3, u5} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) l g) (fun (x : R) (hx : 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.hasMem.{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)))))) x M) => hl (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (FunLike.hasCoeToFun.{succ (max u1 u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toHasLe.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)), Eq.{max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (RingHom.comp.{u2, u4, u6} S Q W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10)) (IsLocalization.map.{u3, u4, u5, u6} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u2, u5, u6} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u3, u5} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) l g) (fun (x : R) (hx : 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.hasMem.{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)))))) x M) => hl (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (FunLike.hasCoeToFun.{succ (max u1 u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u2} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)), Eq.{max (succ u3) (succ u5)} (RingHom.{u3, u5} S W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHom.comp.{u3, u2, u5} S Q W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (IsLocalization.map.{u4, u2, u6, u5} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u3, u4, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u3, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx)))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_comp_map IsLocalization.map_comp_mapₓ'. -/
@@ -1068,7 +1068,7 @@ theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSe
 
 /- warning: is_localization.map_map -> IsLocalization.map_map is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toLE.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)) (x : S), Eq.{succ u6} W (coeFn.{max (succ u4) (succ u6), max (succ u4) (succ u6)} (RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (fun (_x : RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) => Q -> W) (RingHom.hasCoeToFun.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (IsLocalization.map.{u3, u4, u5, u6} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (coeFn.{max (succ u2) (succ u6), max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (fun (_x : RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) => S -> W) (RingHom.hasCoeToFun.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (IsLocalization.map.{u1, u2, u5, u6} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u3, u5} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) l g) (fun (x : R) (hx : 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.hasMem.{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)))))) x M) => hl (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (FunLike.hasCoeToFun.{succ (max u1 u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx))) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toHasLe.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)) (x : S), Eq.{succ u6} W (coeFn.{max (succ u4) (succ u6), max (succ u4) (succ u6)} (RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (fun (_x : RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) => Q -> W) (RingHom.hasCoeToFun.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (IsLocalization.map.{u3, u4, u5, u6} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (coeFn.{max (succ u2) (succ u6), max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (fun (_x : RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) => S -> W) (RingHom.hasCoeToFun.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (IsLocalization.map.{u1, u2, u5, u6} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u3, u5} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) l g) (fun (x : R) (hx : 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.hasMem.{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)))))) x M) => hl (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (FunLike.hasCoeToFun.{succ (max u1 u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx))) x)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u3} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)) (x : S), Eq.{succ u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) => W) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (a : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) a) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u1, u2, u4, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (FunLike.coe.{max (succ u5) (succ u3), succ u3, succ u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W 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(CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u1, u2, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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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(NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx))) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.map_map IsLocalization.map_mapₓ'. -/
@@ -1082,7 +1082,7 @@ theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemirin
 
 /- warning: is_localization.map_smul -> IsLocalization.map_smul is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3))))) z x)) (SMul.smul.{u3, u4} P Q (SMulZeroClass.toHasSmul.{u3, u4} P Q (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} P Q (MulZeroClass.toHasZero.{u3} P (MulZeroOneClass.toMulZeroClass.{u3} P (MonoidWithZero.toMulZeroOneClass.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} P Q (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (Module.toMulActionWithZero.{u3, u4} P Q (CommSemiring.toSemiring.{u3} P _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (Algebra.toModule.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7))))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g z) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (SMul.smul.{u1, u2} R S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3))))) z x)) (SMul.smul.{u3, u4} P Q (SMulZeroClass.toHasSmul.{u3, u4} P Q (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} P Q (MulZeroClass.toHasZero.{u3} P (MulZeroOneClass.toMulZeroClass.{u3} P (MonoidWithZero.toMulZeroOneClass.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} P Q (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (Module.toMulActionWithZero.{u3, u4} P Q (CommSemiring.toSemiring.{u3} P _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (Algebra.toModule.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7))))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g z) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
 but is expected to have type
   forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (HSMul.hSMul.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (instHSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (Algebra.toSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_4 (CommSemiring.toSemiring.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6) _inst_7)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g z) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_smul IsLocalization.map_smulₓ'. -/
@@ -1328,7 +1328,7 @@ include M
 
 /- warning: is_localization.non_zero_divisors_le_comap -> IsLocalization.nonZeroDivisors_le_comap is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Submonoid.comap.{u1, u2, max u1 u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (nonZeroDivisors.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Submonoid.comap.{u1, u2, max u1 u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (nonZeroDivisors.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3], LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (nonZeroDivisors.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))
 Case conversion may be inaccurate. Consider using '#align is_localization.non_zero_divisors_le_comap IsLocalization.nonZeroDivisors_le_comapₓ'. -/
@@ -1347,7 +1347,7 @@ theorem nonZeroDivisors_le_comap [IsLocalization M S] :
 
 /- warning: is_localization.map_non_zero_divisors_le -> IsLocalization.map_nonZeroDivisors_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], LE.le.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Preorder.toLE.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Submonoid.completeLattice.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (Submonoid.map.{u1, u2, max u1 u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (nonZeroDivisors.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], LE.le.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Preorder.toHasLe.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Submonoid.completeLattice.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (Submonoid.map.{u1, u2, max u1 u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (nonZeroDivisors.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3], LE.le.{u1} (Submonoid.{u1} S (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Preorder.toLE.{u1} (Submonoid.{u1} S (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} S (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} S (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} S (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} S (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))))))) (Submonoid.map.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (nonZeroDivisors.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_non_zero_divisors_le IsLocalization.map_nonZeroDivisors_leₓ'. -/
@@ -1832,7 +1832,7 @@ variable {R M} (S) {K : Type _} [IsLocalization M S]
 
 /- warning: is_localization.to_map_eq_zero_iff -> IsLocalization.to_map_eq_zero_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {x : R}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {x : R}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] {x : R}, (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))) (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iffₓ'. -/
@@ -1848,7 +1848,7 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
 
 /- warning: is_localization.injective -> IsLocalization.injective is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Function.Injective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align is_localization.injective IsLocalization.injectiveₓ'. -/
@@ -1861,7 +1861,7 @@ protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraM
 
 /- warning: is_localization.to_map_ne_zero_of_mem_non_zero_divisors -> IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisors is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {x : R}, (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {x : R}, (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall {x : R}, (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.to_map_ne_zero_of_mem_non_zero_divisors IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisorsₓ'. -/
@@ -1875,7 +1875,7 @@ variable {S}
 
 /- warning: is_localization.sec_snd_ne_zero -> IsLocalization.sec_snd_ne_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall (x : S), Ne.{succ u1} R ((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 (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x M))))) (Prod.snd.{u1, u1} R (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) (IsLocalization.sec.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 _inst_5 x))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall (x : S), Ne.{succ u1} R ((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 (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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_inst_5 x))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall (x : S), Ne.{succ u2} R (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) (Prod.snd.{u2, u2} R (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 M)) (IsLocalization.sec.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 _inst_5 x))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_snd_ne_zero IsLocalization.sec_snd_ne_zeroₓ'. -/
@@ -1886,7 +1886,7 @@ theorem sec_snd_ne_zero [Nontrivial R] (hM : M ≤ nonZeroDivisors R) (x : S) :
 
 /- warning: is_localization.sec_fst_ne_zero -> IsLocalization.sec_fst_ne_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R] [_inst_7 : NoZeroDivisors.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_2))) (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_2))))))], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {x : S}, (Ne.{succ u2} S 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_2)))))))))) -> (Ne.{succ u1} R (Prod.fst.{u1, u1} R (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) (IsLocalization.sec.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 _inst_5 x)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R] [_inst_7 : NoZeroDivisors.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_2))) (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_2))))))], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {x : S}, (Ne.{succ u2} S 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_2)))))))))) -> (Ne.{succ u1} R (Prod.fst.{u1, u1} R (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) (IsLocalization.sec.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 _inst_5 x)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R] [_inst_7 : NoZeroDivisors.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall {x : S}, (Ne.{succ u1} S x (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) -> (Ne.{succ u2} R (Prod.fst.{u2, u2} R (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 M)) (IsLocalization.sec.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 _inst_5 x)) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zeroₓ'. -/
@@ -1931,7 +1931,7 @@ variable (A : Type _) [CommRing A] [IsDomain A]
 
 /- warning: is_localization.no_zero_divisors_of_le_non_zero_divisors -> IsLocalization.noZeroDivisors_of_le_nonZeroDivisors is a dubious translation:
 lean 3 declaration is
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.completeLattice.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (NoZeroDivisors.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2))) (MulZeroClass.toHasZero.{u1} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toHasLe.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.completeLattice.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (NoZeroDivisors.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2))) (MulZeroClass.toHasZero.{u1} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))
 but is expected to have type
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8))))) -> (NoZeroDivisors.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))
 Case conversion may be inaccurate. Consider using '#align is_localization.no_zero_divisors_of_le_non_zero_divisors IsLocalization.noZeroDivisors_of_le_nonZeroDivisorsₓ'. -/
@@ -1957,7 +1957,7 @@ theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [Is
 
 /- warning: is_localization.is_domain_of_le_non_zero_divisors -> IsLocalization.isDomain_of_le_nonZeroDivisors is a dubious translation:
 lean 3 declaration is
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.completeLattice.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toHasLe.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.completeLattice.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))
 but is expected to have type
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8))))) -> (IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_localization.is_domain_of_le_non_zero_divisors IsLocalization.isDomain_of_le_nonZeroDivisorsₓ'. -/
@@ -1980,7 +1980,7 @@ variable {A}
 
 /- warning: is_localization.is_domain_localization -> IsLocalization.isDomain_localization is a dubious translation:
 lean 3 declaration is
-  forall {A : Type.{u1}} [_inst_8 : CommRing.{u1} A] [_inst_9 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))] {M : Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))}, (LE.le.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Preorder.toLE.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Submonoid.completeLattice.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))))))) M (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))))) -> (IsDomain.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Ring.toSemiring.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (CommRing.toRing.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Localization.commRing.{u1} A _inst_8 M))))
+  forall {A : Type.{u1}} [_inst_8 : CommRing.{u1} A] [_inst_9 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))] {M : Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))}, (LE.le.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Submonoid.completeLattice.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))))))) M (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))))) -> (IsDomain.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Ring.toSemiring.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (CommRing.toRing.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Localization.commRing.{u1} A _inst_8 M))))
 but is expected to have type
   forall {A : Type.{u1}} [_inst_8 : CommRing.{u1} A] [_inst_9 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8))] {M : Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))}, (LE.le.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (Preorder.toLE.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))))))) M (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8))))) -> (IsDomain.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8) M)))
 Case conversion may be inaccurate. Consider using '#align is_localization.is_domain_localization IsLocalization.isDomain_localizationₓ'. -/
@@ -2105,7 +2105,7 @@ variable (M)
 
 /- warning: is_localization.algebra_map_eq_map_map_submonoid -> IsLocalization.algebraMap_eq_map_map_submonoid is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))], Eq.{max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))], Eq.{max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u4}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u4} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u4, u3} R Rₘ Sₘ (Algebra.toSMul.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u3} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u4} Rₘ (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (algebraMap.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u2, u4, u1, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3))]))
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_eq_map_map_submonoid IsLocalization.algebraMap_eq_map_map_submonoidₓ'. -/
@@ -2127,7 +2127,7 @@ theorem IsLocalization.algebraMap_eq_map_map_submonoid :
 
 /- warning: is_localization.algebra_map_apply_eq_map_map_submonoid -> IsLocalization.algebraMap_apply_eq_map_map_submonoid is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : Rₘ), Eq.{succ u4} Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))) x)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : Rₘ), Eq.{succ u4} Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))) x)
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u4} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u3, u4} R Rₘ Sₘ (Algebra.toSMul.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u4} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] (x : Rₘ), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (IsLocalization.map.{u2, u3, u1, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3))])) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoidₓ'. -/

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

@@ -1158,7 +1158,7 @@ theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T) (x : R) (y : 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)))))) M), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingEquiv.{u2, u4} S Q 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(NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasMul.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))) (Distrib.toHasAdd.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.ringEquivOfRingEquiv.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 j H) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u3, u4} P _inst_4 T Q _inst_6 _inst_7 _inst_8 (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R 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 but is expected to have type
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(NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y)) T H)])))
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u4, u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u4, u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T) (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M)), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : S) => Q) (IsLocalization.mk'.{u4, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) 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(NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))))) j) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y) (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{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 _inst_1))))) M) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y)) T H)])))
 Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_mk' IsLocalization.ringEquivOfRingEquiv_mk'ₓ'. -/
 theorem ringEquivOfRingEquiv_mk' {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x : R) (y : M) :
     ringEquivOfRingEquiv S Q j H (mk' S x y) =

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

@@ -1766,7 +1766,7 @@ instance : Neg (Localization M) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (a : R) (b : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Neg.neg.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.hasNeg.{u1} R _inst_1 M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) a) b)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (a : R) (b : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Neg.neg.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instNegLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) a) b)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : 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)))))} (a : R) (b : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Neg.neg.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instNegLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) a) b)
 Case conversion may be inaccurate. Consider using '#align localization.neg_mk Localization.neg_mkₓ'. -/
 theorem neg_mk (a b) : -(mk a b : Localization M) = mk (-a) b :=
   by
@@ -1803,7 +1803,7 @@ instance : CommRing (Localization M) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (a : R) (c : R) (b : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) (d : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (HSub.hSub.{u1, u1, u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (instHSub.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (SubNegMonoid.toHasSub.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (AddGroup.toSubNegMonoid.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (AddGroupWithOne.toAddGroup.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Ring.toAddCommGroupWithOne.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.commRing.{u1} R _inst_1 M)))))))) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M c d)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((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 (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R 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(SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R 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 but is expected to have type
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(Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (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 (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) M)) d) a) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (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 (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) M)) b) c)) (HMul.hMul.{u1, u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (instHMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (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))))) M)) b d))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : 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)))))} (a : R) (c : R) (b : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (d : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (HSub.hSub.{u1, u1, u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (instHSub.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Ring.toSub.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} R _inst_1 M)))) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M c d)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (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 (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) M)) d) a) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (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 (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) M)) b) c)) (HMul.hMul.{u1, u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (instHMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (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))))) M)) b d))
 Case conversion may be inaccurate. Consider using '#align localization.sub_mk Localization.sub_mkₓ'. -/
 theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b * c) (b * d) :=
   calc
@@ -1818,7 +1818,7 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (m : Int), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) m) (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) (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))))) M))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (HasLiftT.mk.{1, succ u1} Int (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CoeTCₓ.coe.{1, succ u1} Int (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Int.castCoe.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (AddGroupWithOne.toHasIntCast.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Ring.toAddCommGroupWithOne.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.commRing.{u1} R _inst_1 M)))))))) m)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (m : Int), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Int.cast.{u1} R (Ring.toIntCast.{u1} R (CommRing.toRing.{u1} R _inst_1)) m) (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (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))))) M)))) (Int.cast.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Ring.toIntCast.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} R _inst_1 M))) m)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : 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 : Int), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Int.cast.{u1} R (Ring.toIntCast.{u1} R (CommRing.toRing.{u1} R _inst_1)) m) (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (Submonoid.one.{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)))) (Int.cast.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Ring.toIntCast.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} R _inst_1 M))) m)
 Case conversion may be inaccurate. Consider using '#align localization.mk_int_cast Localization.mk_int_castₓ'. -/
 theorem mk_int_cast (m : ℤ) : (mk m 1 : Localization M) = m := by
   simpa using @mk_algebra_map R _ M ℤ _ _ m
@@ -1834,7 +1834,7 @@ variable {R M} (S) {K : Type _} [IsLocalization M S]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {x : R}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] {x : R}, (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))) (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] {x : R}, (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))) (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iffₓ'. -/
 theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R S x = 0 ↔ x = 0 :=
   by
@@ -1850,7 +1850,7 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Function.Injective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3)))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Function.Injective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align is_localization.injective IsLocalization.injectiveₓ'. -/
 protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraMap R S) :=
   by
@@ -1863,7 +1863,7 @@ protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraM
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {x : R}, (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (forall {x : R}, (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) x (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall {x : R}, (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) x (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.to_map_ne_zero_of_mem_non_zero_divisors IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisorsₓ'. -/
 protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M ≤ nonZeroDivisors R)
     {x : R} (hx : x ∈ nonZeroDivisors R) : algebraMap R S x ≠ 0 :=
@@ -1877,7 +1877,7 @@ variable {S}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall (x : S), Ne.{succ u1} R ((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 (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) R (coeBase.{succ u1, succ u1} (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) R (coeSubtype.{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.hasMem.{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.setLike.{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 M))))) (Prod.snd.{u1, u1} R (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) (IsLocalization.sec.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 _inst_5 x))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (forall (x : S), Ne.{succ u2} R (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) (Prod.snd.{u2, u2} R (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 M)) (IsLocalization.sec.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 _inst_5 x))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall (x : S), Ne.{succ u2} R (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) (Prod.snd.{u2, u2} R (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 M)) (IsLocalization.sec.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 _inst_5 x))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_snd_ne_zero IsLocalization.sec_snd_ne_zeroₓ'. -/
 theorem sec_snd_ne_zero [Nontrivial R] (hM : M ≤ nonZeroDivisors R) (x : S) :
     ((sec M x).snd : R) ≠ 0 :=
@@ -1888,7 +1888,7 @@ theorem sec_snd_ne_zero [Nontrivial R] (hM : M ≤ nonZeroDivisors R) (x : S) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R] [_inst_7 : NoZeroDivisors.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_2))) (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_2))))))], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {x : S}, (Ne.{succ u2} S 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_2)))))))))) -> (Ne.{succ u1} R (Prod.fst.{u1, u1} R (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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{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 (CommRing.toCommSemiring.{u1} R _inst_1))))))) M) (IsLocalization.sec.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 _inst_5 x)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R] [_inst_7 : NoZeroDivisors.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (forall {x : S}, (Ne.{succ u1} S x (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) -> (Ne.{succ u2} R (Prod.fst.{u2, u2} R (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 M)) (IsLocalization.sec.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 _inst_5 x)) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R] [_inst_7 : NoZeroDivisors.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))], (LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall {x : S}, (Ne.{succ u1} S x (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) -> (Ne.{succ u2} R (Prod.fst.{u2, u2} R (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 M)) (IsLocalization.sec.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 _inst_5 x)) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zeroₓ'. -/
 theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDivisors R) {x : S}
     (hx : x ≠ 0) : (sec M x).fst ≠ 0 :=
@@ -1906,7 +1906,7 @@ variable (S M) (Q : Type _) [CommRing Q] {g : R →+* P} [Algebra P Q]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] (Q : Type.{u4}) [_inst_6 : CommRing.{u4} Q] {g : RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u4} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (Ring.toSemiring.{u4} Q (CommRing.toRing.{u4} Q _inst_6))], (Function.Injective.{succ u1, succ u3} R P (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (fun (_x : RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u4} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7], Function.Injective.{succ u2, succ u4} S Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (IsLocalization.map.{u1, u2, u3, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] (Q : Type.{u2}) [_inst_6 : CommRing.{u2} Q] {g : RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u2} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (Ring.toSemiring.{u2} Q (CommRing.toRing.{u2} Q _inst_6))], (Function.Injective.{succ u4, succ u3} R P (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u2} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7], Function.Injective.{succ u1, succ u2} S Q (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))) (RingHom.instRingHomClassRingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))))) (IsLocalization.map.{u4, u1, u3, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{max u4 u3, u3, u4} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] (Q : Type.{u2}) [_inst_6 : CommRing.{u2} Q] {g : RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u2} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))], (Function.Injective.{succ u4, succ u3} R P (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (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} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u2} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7], Function.Injective.{succ u1, succ u2} S Q (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))) (RingHom.instRingHomClassRingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))))) (IsLocalization.map.{u4, u1, u3, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{max u4 u3, u3, u4} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injectiveₓ'. -/
 /-- Injectivity of a map descends to the map induced on localizations. -/
 theorem map_injective_of_injective (hg : Function.Injective g)
@@ -1933,7 +1933,7 @@ variable (A : Type _) [CommRing A] [IsDomain A]
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.completeLattice.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (NoZeroDivisors.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2))) (MulZeroClass.toHasZero.{u1} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (NoZeroDivisors.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8))))) -> (NoZeroDivisors.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))
 Case conversion may be inaccurate. Consider using '#align is_localization.no_zero_divisors_of_le_non_zero_divisors IsLocalization.noZeroDivisors_of_le_nonZeroDivisorsₓ'. -/
 /-- A `comm_ring` `S` which is the localization of a ring `R` without zero divisors at a subset of
 non-zero elements does not have zero divisors.
@@ -1959,7 +1959,7 @@ theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [Is
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.completeLattice.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_8))))) -> (IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_localization.is_domain_of_le_non_zero_divisors IsLocalization.isDomain_of_le_nonZeroDivisorsₓ'. -/
 /-- A `comm_ring` `S` which is the localization of an integral domain `R` at a subset of
 non-zero elements is an integral domain.
@@ -1982,7 +1982,7 @@ variable {A}
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_8 : CommRing.{u1} A] [_inst_9 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))] {M : Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))}, (LE.le.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Preorder.toLE.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Submonoid.completeLattice.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))))))) M (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))))) -> (IsDomain.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Ring.toSemiring.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (CommRing.toRing.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Localization.commRing.{u1} A _inst_8 M))))
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_8 : CommRing.{u1} A] [_inst_9 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))] {M : Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))}, (LE.le.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Preorder.toLE.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))))))) M (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))))) -> (IsDomain.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Ring.toSemiring.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (CommRing.toRing.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} A _inst_8 M))))
+  forall {A : Type.{u1}} [_inst_8 : CommRing.{u1} A] [_inst_9 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8))] {M : Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))}, (LE.le.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (Preorder.toLE.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8)))))))))) M (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8))))) -> (IsDomain.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} A (CommRing.toCommSemiring.{u1} A _inst_8) M)))
 Case conversion may be inaccurate. Consider using '#align is_localization.is_domain_localization IsLocalization.isDomain_localizationₓ'. -/
 /-- The localization at of an integral domain to a set of non-zero elements is an integral domain.
 See note [reducible non-instances]. -/
@@ -2000,7 +2000,7 @@ open IsLocalization
 lean 3 declaration is
   forall {R : Type.{u1}} {Rₘ : Type.{u2}} [_inst_5 : CommRing.{u1} R] [_inst_6 : CommRing.{u2} Rₘ] {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_5)))))}, (Not (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_5)))))) (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_5)))))) 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_5))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))))) M)) -> (IsField.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) -> (forall [_inst_7 : Algebra.{u1, u2} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u1, succ u2} R Rₘ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) (fun (_x : RingHom.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) => R -> Rₘ) (RingHom.hasCoeToFun.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) (algebraMap.{u1, u2} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)) _inst_7)))
 but is expected to have type
-  forall {R : Type.{u2}} {Rₘ : Type.{u1}} [_inst_5 : CommRing.{u2} R] [_inst_6 : CommRing.{u1} Rₘ] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))}, (Not (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) M)) -> (IsField.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5))) -> (forall [_inst_7 : Algebra.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} R Rₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Rₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))))))) (algebraMap.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)) _inst_7)))
+  forall {R : Type.{u2}} {Rₘ : Type.{u1}} [_inst_5 : CommRing.{u2} R] [_inst_6 : CommRing.{u1} Rₘ] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))}, (Not (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_5)))))) (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_5)))))) 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_5))))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) M)) -> (IsField.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) -> (forall [_inst_7 : Algebra.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} R Rₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Rₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R Rₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)))) R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6))))))) (algebraMap.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u1} Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6)) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align is_field.localization_map_bijective IsField.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommRing Rₘ]
@@ -2019,7 +2019,7 @@ theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommR
 lean 3 declaration is
   forall {K : Type.{u1}} {Kₘ : Type.{u2}} [_inst_5 : Field.{u1} K] [_inst_6 : CommRing.{u2} Kₘ] {M : Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))}, (Not (Membership.Mem.{u1, u1} K (Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))) K (Submonoid.setLike.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))))))) M)) -> (forall [_inst_7 : Algebra.{u1, u2} K Kₘ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u1, u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u2} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u1, succ u2} K Kₘ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) (fun (_x : RingHom.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) => K -> Kₘ) (RingHom.hasCoeToFun.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) (algebraMap.{u1, u2} K Kₘ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)) _inst_7)))
 but is expected to have type
-  forall {K : Type.{u2}} {Kₘ : Type.{u1}} [_inst_5 : Field.{u2} K] [_inst_6 : CommRing.{u1} Kₘ] {M : Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))}, (Not (Membership.mem.{u2, u2} K (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))) K (Submonoid.instSetLikeSubmonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))))) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) M)) -> (forall [_inst_7 : Algebra.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} K Kₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Kₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) (NonUnitalNonAssocSemiring.toMul.{u1} Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))))))) (algebraMap.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)) _inst_7)))
+  forall {K : Type.{u2}} {Kₘ : Type.{u1}} [_inst_5 : Field.{u2} K] [_inst_6 : CommRing.{u1} Kₘ] {M : Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))))}, (Not (Membership.mem.{u2, u2} K (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))))) K (Submonoid.instSetLikeSubmonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))))) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) M)) -> (forall [_inst_7 : Algebra.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} K Kₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Kₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K Kₘ (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) (NonUnitalNonAssocSemiring.toMul.{u1} Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)))) K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6))))))) (algebraMap.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (CommSemiring.toSemiring.{u1} Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6)) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align field.localization_map_bijective Field.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem Field.localization_map_bijective {K Kₘ : Type _} [Field K] [CommRing Kₘ] {M : Submonoid K}
@@ -2074,7 +2074,7 @@ include S
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Sₘ : Type.{u3}) [_inst_6 : CommRing.{u3} Sₘ] [_inst_9 : Algebra.{u2, u3} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u3} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u1, u2, u3} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} S Sₘ (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u3} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (Algebra.toModule.{u2, u3} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u3} R Sₘ (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Sₘ (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.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u3} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (Algebra.toModule.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)))))] (y : 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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Sₘ _inst_6)))) => R -> Sₘ) (RingHom.hasCoeToFun.{u1, u3} R Sₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) (algebraMap.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12) ((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))))))) M) 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))))))) M) 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))))))) M) 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))))))) M) 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 M))))) y))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] (Sₘ : Type.{u1}) [_inst_6 : CommRing.{u1} Sₘ] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u2, u3, u1} R S Sₘ (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3) (Algebra.toSMul.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_12)] (y : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) x M)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 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(CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_12) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : 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)))))} (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] (Sₘ : Type.{u1}) [_inst_6 : CommRing.{u1} Sₘ] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u2, u3, u1} R S Sₘ (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) (Algebra.toSMul.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_12)] (y : 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 M)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y)) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) _inst_12) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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)))))) M)) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoidₓ'. -/
 theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R Sₘ y) :=
   by
@@ -2086,7 +2086,7 @@ theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R S
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : R) (y : 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))))))) M), Eq.{succ u4} Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ 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_inst_10 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u2} S (fun (x : S) => Membership.Mem.{u2, u2} S (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) S (Submonoid.setLike.{u2} S (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))))) x (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{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))))))) M) 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))))))) M) 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))))))) M) 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 M))))) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M y)))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u4, u2, u3} R Rₘ Sₘ (Algebra.toSMul.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u4, u1, u3} R S Sₘ (Algebra.toSMul.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] (x : R) (y : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))))) x M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))))) (algebraMap.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u1, u3} ((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_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2))))))) x_1 (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (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 (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) M)) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u4} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M y)))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : 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)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u4, u2, u3} R Rₘ Sₘ (Algebra.toSMul.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u4, u1, u3} R S Sₘ (Algebra.toSMul.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] (x : R) (y : 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 M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))))))) (algebraMap.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u1, u3} ((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_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2))))))) x_1 (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (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)))))) M)) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u4} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M y)))
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_mk' IsLocalization.algebraMap_mk'ₓ'. -/
 @[simp]
 theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
@@ -2107,7 +2107,7 @@ variable (M)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))], Eq.{max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u4}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u4} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Rₘ (CommRing.toRing.{u4} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u4, u3} R Rₘ Sₘ (Algebra.toSMul.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Rₘ (CommRing.toRing.{u4} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u3} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u4} Rₘ (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) (algebraMap.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u2, u4, u1, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3))]))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u4}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u4} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u4, u3} R Rₘ Sₘ (Algebra.toSMul.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u3} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u4} Rₘ (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (algebraMap.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u2, u4, u1, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3))]))
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_eq_map_map_submonoid IsLocalization.algebraMap_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
@@ -2129,7 +2129,7 @@ theorem IsLocalization.algebraMap_eq_map_map_submonoid :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : Rₘ), Eq.{succ u4} Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u4} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u3, u4} R Rₘ Sₘ (Algebra.toSMul.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u4} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)] (x : Rₘ), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (IsLocalization.map.{u2, u3, u1, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3))])) x)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u4} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u3, u4} R Rₘ Sₘ (Algebra.toSMul.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u4} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_12)] (x : Rₘ), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)) _inst_11) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (IsLocalization.map.{u2, u3, u1, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3))])) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
@@ -2151,7 +2151,7 @@ variable {R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))], Eq.{max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (IsLocalization.lift.{u1, u3, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_8 (algebraMap.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12) (IsLocalization.map_units_map_submonoid.{u1, u2, u4} R _inst_1 M S _inst_2 _inst_3 Sₘ _inst_6 _inst_9 _inst_10 _inst_12 _inst_14)) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u4}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u4} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Rₘ (CommRing.toRing.{u4} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u4, u3} R Rₘ Sₘ (Algebra.toSMul.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Rₘ (CommRing.toRing.{u4} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u3} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u4} Rₘ (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (IsLocalization.lift.{u2, u4, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7 Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_8 (algebraMap.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12) (IsLocalization.map_units_map_submonoid.{u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Sₘ _inst_6 _inst_9 _inst_10 _inst_12 _inst_14)) (algebraMap.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : 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)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] (Rₘ : Type.{u4}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u4} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u4, u3} R Rₘ Sₘ (Algebra.toSMul.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u3} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12)], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u4} Rₘ (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (IsLocalization.lift.{u2, u4, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7 Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_8 (algebraMap.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_12) (IsLocalization.map_units_map_submonoid.{u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Sₘ _inst_6 _inst_9 _inst_10 _inst_12 _inst_14)) (algebraMap.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)) _inst_11)
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_algebra_map_eq_algebra_map IsLocalization.lift_algebraMap_eq_algebraMapₓ'. -/
 theorem IsLocalization.lift_algebraMap_eq_algebraMap :
     @IsLocalization.lift R _ M Rₘ _ _ Sₘ _ _ (algebraMap R Sₘ)
@@ -2168,7 +2168,7 @@ variable (Rₘ Sₘ)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u3, succ u4} Rₘ Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) (localizationAlgebra.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))} {S : Type.{u3}} [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u1}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u1} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u4, succ u3} R S (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (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} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))))) (algebraMap.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u2, succ u1} Rₘ Sₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) (localizationAlgebra.{u4, u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : 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)))))} {S : Type.{u3}} [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u1}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u1} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u4, succ u3} R S (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (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} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))))))) (algebraMap.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u2, succ u1} Rₘ Sₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (CommSemiring.toSemiring.{u1} Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6)) (localizationAlgebra.{u4, u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
 Case conversion may be inaccurate. Consider using '#align localization_algebra_injective localizationAlgebra_injectiveₓ'. -/
 /-- Injectivity of the underlying `algebra_map` descends to the algebra induced by localization. -/
 theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -1158,7 +1158,7 @@ theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T) (x : R) (y : 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)))))) M), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingEquiv.{u2, u4} S Q 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(SetLike.hasMem.{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)))))) x M))))) y) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} 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_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)))))) x M) y))))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u4, u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u4, u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u4, u3} R P 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(NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u2} Q (NonUnitalNonAssocSemiring.toDistrib.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))))) (RingEquiv.instRingEquivClassRingEquiv.{u1, u2} S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Distrib.toAdd.{u2} Q 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+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T) (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M)), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : S) => Q) (IsLocalization.mk'.{u4, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) 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(CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))))) j (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y)) x._@.Mathlib.RingTheory.Localization.Basic._hyg.8175) (Set.mem_image_of_mem.{u3, u4} R P (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (EquivLike.toEmbeddingLike.{max (succ u4) (succ u3), succ u4, succ u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (MulEquivClass.toEquivLike.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingEquivClass.toMulEquivClass.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))))) j) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y) (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{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 _inst_1))))) M) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y)) T H)])))
 Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_mk' IsLocalization.ringEquivOfRingEquiv_mk'ₓ'. -/
 theorem ringEquivOfRingEquiv_mk' {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x : R) (y : M) :
     ringEquivOfRingEquiv S Q j H (mk' S x y) =

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61

@@ -1431,12 +1431,12 @@ private unsafe def tac :=
   sorry
 #align localization.tac localization.tac
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2028012893.tac -/
 instance : CommSemiring (Localization M) :=
   { Localization.commMonoidWithZero M with
     zero := 0

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

@@ -742,7 +742,7 @@ theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (h : forall (y : 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 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 but is expected to have type
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+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] {g : RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} (h : forall (y : 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 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M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} 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R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) z₁)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) P ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) z₂))
 Case conversion may be inaccurate. Consider using '#align is_localization.mul_add_inv_left IsLocalization.mul_add_inv_leftₓ'. -/
 theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (w z₁ z₂ : P) :
     w * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) h y)⁻¹ + z₁ = z₂ ↔ w + g y * z₁ = g y * z₂ :=
@@ -801,7 +801,7 @@ variable {g : R →+* P} (hg : ∀ y : M, IsUnit (g y))
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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M) hg) y))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (fun (_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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) => Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MulOneClass.toMul.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M))) (MulOneClass.toMul.{u2} (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MonoidHom.monoidHomClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))))) (IsUnit.liftRight.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) P (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M) (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (MonoidHom.restrict.{u3, u2, u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) P (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instSubmonoidClassSubmonoidInstSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (RingHom.toMonoidHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) g) M) hg) y))))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _inst_1))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R 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 Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk' IsLocalization.lift_mk'ₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from

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

@@ -1604,7 +1604,7 @@ theorem toLocalizationMap_eq_monoidOf : toLocalizationMap M (Localization M) = m
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (fun (_x : MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) => R -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (MonoidHom.hasCoeToFun.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (Submonoid.LocalizationMap.toMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (fun (_x : RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) => R -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (RingHom.hasCoeToFun.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M))) (MonoidHom.monoidHomClass.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))))) (Submonoid.LocalizationMap.toMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M))) (MonoidHom.monoidHomClass.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))))) (Submonoid.LocalizationMap.toMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align localization.monoid_of_eq_algebra_map Localization.monoidOf_eq_algebraMapₓ'. -/
 theorem monoidOf_eq_algebraMap (x) : (monoidOf M).toMap x = algebraMap R (Localization M) x :=
   rfl

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

@@ -101,9 +101,9 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 variable [Algebra R S] {P : Type _} [CommSemiring P]
 
 #print IsLocalization /-
-/- ./././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 typeclass `is_localization (M : submodule R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
 class IsLocalization : Prop where

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

@@ -1764,7 +1764,7 @@ instance : Neg (Localization M) :=
 
 /- warning: localization.neg_mk -> Localization.neg_mk is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (a : R) (b : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Neg.neg.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.hasNeg.{u1} R _inst_1 M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) a) b)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (a : R) (b : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Neg.neg.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.hasNeg.{u1} R _inst_1 M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) a) b)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (a : R) (b : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Neg.neg.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instNegLocalizationToCommMonoid.{u1} R _inst_1 M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) a) b)
 Case conversion may be inaccurate. Consider using '#align localization.neg_mk Localization.neg_mkₓ'. -/
@@ -1801,7 +1801,7 @@ instance : CommRing (Localization M) :=
 
 /- warning: localization.sub_mk -> Localization.sub_mk is a dubious translation:
 lean 3 declaration is
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(CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) (instHMul.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) (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))))) M)) b d))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (a : R) (c : R) (b : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (d : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (HSub.hSub.{u1, u1, u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (instHSub.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Ring.toSub.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} R _inst_1 M)))) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M a b) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M c d)) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (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 (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) M)) d) a) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (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 (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) M)) b) c)) (HMul.hMul.{u1, u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (instHMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (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))))) M)) b d))
 Case conversion may be inaccurate. Consider using '#align localization.sub_mk Localization.sub_mkₓ'. -/
@@ -1816,7 +1816,7 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b
 
 /- warning: localization.mk_int_cast -> Localization.mk_int_cast is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (m : Int), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) m) (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) (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))))) M))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (HasLiftT.mk.{1, succ u1} Int (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CoeTCₓ.coe.{1, succ u1} Int (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Int.castCoe.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (AddGroupWithOne.toHasIntCast.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (NonAssocRing.toAddGroupWithOne.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Ring.toNonAssocRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.commRing.{u1} R _inst_1 M)))))))) m)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (m : Int), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) m) (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) M) (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))))) M))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (HasLiftT.mk.{1, succ u1} Int (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CoeTCₓ.coe.{1, succ u1} Int (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Int.castCoe.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (AddGroupWithOne.toHasIntCast.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (AddCommGroupWithOne.toAddGroupWithOne.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Ring.toAddCommGroupWithOne.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.commRing.{u1} R _inst_1 M)))))))) m)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (m : Int), Eq.{succ u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M (Int.cast.{u1} R (Ring.toIntCast.{u1} R (CommRing.toRing.{u1} R _inst_1)) m) (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) x M)) (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))))) M)))) (Int.cast.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Ring.toIntCast.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} R _inst_1 M))) m)
 Case conversion may be inaccurate. Consider using '#align localization.mk_int_cast Localization.mk_int_castₓ'. -/

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

@@ -487,7 +487,7 @@ theorem mk'_eq_iff_eq' {x₁ x₂} {y₁ y₂ : M} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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)))))) M} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)}, Iff (Membership.Mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) I) (Membership.Mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) I)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)}, Iff (Membership.mem.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.instSetLikeSubmodule.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) I) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.instSetLikeSubmodule.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) I)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)}, Iff (Membership.mem.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) I) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) I)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iffₓ'. -/
 theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R S x ∈ I :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -1228,7 +1228,7 @@ theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃
     IsLocalization M P := by
   constructor
   · intro y
-    convert (IsLocalization.map_units S y).map h.to_alg_hom.to_ring_hom.to_monoid_hom
+    convert(IsLocalization.map_units S y).map h.to_alg_hom.to_ring_hom.to_monoid_hom
     exact (h.commutes y).symm
   · intro y
     obtain ⟨⟨x, s⟩, e⟩ := IsLocalization.surj M (h.symm y)
@@ -1310,7 +1310,7 @@ theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
   refine' ⟨fun _ => is_localization_of_base_ring_equiv _ _ h, _⟩
   letI := ((algebraMap R S).comp h.symm.to_ring_hom).toAlgebra
   intro H
-  convert @is_localization_of_base_ring_equiv _ _ _ _ _ _ H h.symm
+  convert@is_localization_of_base_ring_equiv _ _ _ _ _ _ H h.symm
   · erw [Submonoid.map_equiv_eq_comap_symm, Submonoid.comap_map_eq_of_injective]
     exact h.to_equiv.injective
   rw [RingHom.algebraMap_toAlgebra, RingHom.comp_assoc]

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
 
 ! This file was ported from Lean 3 source module ring_theory.localization.basic
-! leanprover-community/mathlib commit b69c9a770ecf37eb21f7b8cf4fa00de3b62694ec
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Tactic.RingExp
 /-!
 # Localizations of commutative rings
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We characterize the localization of a commutative ring `R` at a submonoid `M` up to
 isomorphism; that is, a commutative ring `S` is the localization of `R` at `M` iff we can find a
 ring homomorphism `f : R →+* S` satisfying 3 properties:
@@ -1428,12 +1431,12 @@ private unsafe def tac :=
   sorry
 #align localization.tac localization.tac
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.709738471.tac -/
 instance : CommSemiring (Localization M) :=
   { Localization.commMonoidWithZero M with
     zero := 0

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

@@ -126,7 +126,7 @@ variable (M)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M N) -> (forall (r : 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.hasMem.{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)))))) r N) -> (IsUnit.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r))) -> (IsLocalization.{u1, u2} R _inst_1 N S _inst_2 _inst_3)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))), (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M N) -> (forall (r : 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)))))) r N) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) r))) -> (IsLocalization.{u2, u1} R _inst_1 N S _inst_2 _inst_3)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))), (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M N) -> (forall (r : 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)))))) r N) -> (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) r))) -> (IsLocalization.{u2, u1} R _inst_1 N S _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align is_localization.of_le IsLocalization.of_leₓ'. -/
 theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (algebraMap R S r)) :
     IsLocalization N S :=
@@ -181,7 +181,7 @@ theorem toLocalizationMap_toMap : (toLocalizationMap M S).toMap = (algebraMap R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} S (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) (fun (_x : MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) => R -> S) (MonoidHom.hasCoeToFun.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) (Submonoid.LocalizationMap.toMap.{u1, u2} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M S (CommSemiring.toCommMonoid.{u2} S _inst_2) (IsLocalization.toLocalizationMap.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R S (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))))) (Submonoid.LocalizationMap.toMap.{u1, u2} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M S (CommSemiring.toCommMonoid.{u2} S _inst_2) (IsLocalization.toLocalizationMap.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R S (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u2} S (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))) R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2))) (MonoidHom.monoidHomClass.{u1, u2} R S (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u2} S (CommMonoid.toMonoid.{u2} S (CommSemiring.toCommMonoid.{u2} S _inst_2)))))) (Submonoid.LocalizationMap.toMap.{u1, u2} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M S (CommSemiring.toCommMonoid.{u2} S _inst_2) (IsLocalization.toLocalizationMap.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.to_localization_map_to_map_apply IsLocalization.toLocalizationMap_toMap_applyₓ'. -/
 theorem toLocalizationMap_toMap_apply (x) : (toLocalizationMap M S).toMap x = algebraMap R S x :=
   rfl
@@ -218,7 +218,7 @@ theorem toLocalizationMap_sec : (toLocalizationMap M S).sec = sec M :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) (Prod.snd.{u1, u1} R (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)))))) M) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (Prod.fst.{u1, u1} R (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)))))) M) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))
 but is expected to have type
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(CommSemiring.toSemiring.{u2} S _inst_2))))) z (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_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))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (Prod.fst.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (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))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) z (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_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))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (Prod.fst.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_spec IsLocalization.sec_specₓ'. -/
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x` (so this lemma is true by definition). -/
@@ -231,7 +231,7 @@ theorem sec_spec (z : S) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (Prod.fst.{u1, u1} R (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)))))) M) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) (Prod.snd.{u1, u1} R (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)))))) M) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) z)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Prod.fst.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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_inst_1))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) _inst_2))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_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))))) M)) (Prod.snd.{u1, u1} R (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 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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Prod.fst.{u1, u1} R (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 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_inst_1))))) M)) (Prod.snd.{u1, u1} R (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 M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) _inst_2))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S 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(NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x M)) (IsLocalization.sec.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 z)))) z)
 Case conversion may be inaccurate. Consider using '#align is_localization.sec_spec' IsLocalization.sec_spec'ₓ'. -/
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x`, so this lemma is just an application of `S`'s commutativity. -/
@@ -246,7 +246,7 @@ variable {R M}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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} 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((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 (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 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_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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) c) y))) -> (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} 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(CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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 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(fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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 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(CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c) y))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_right_cancel IsLocalization.map_right_cancelₓ'. -/
 theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap R S (c * y)) :
     algebraMap R S x = algebraMap R S y :=
@@ -257,7 +257,7 @@ theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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} 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_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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) c)))) -> (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R 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 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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 M)}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c))) (FunLike.coe.{max (succ u2) (succ u1), succ 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_inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) y (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : R} {c : 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 M)}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c))) (FunLike.coe.{max (succ u2) (succ u1), succ 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_inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) y (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) c)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_left_cancel IsLocalization.map_left_cancelₓ'. -/
 theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R S (y * c)) :
     algebraMap R S x = algebraMap R S y :=
@@ -268,7 +268,7 @@ theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {z : S} {x : R} {y : 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)))))) M}, (Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) -> (Eq.{succ u2} S z (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {z : S} {x : R} {y : 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 M)}, (Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) -> (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} S z (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2)))))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {z : S} {x : R} {y : 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 M)}, (Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) -> (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))) -> (Eq.{succ u1} S z (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align is_localization.eq_zero_of_fst_eq_zero IsLocalization.eq_zero_of_fst_eq_zeroₓ'. -/
 theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebraMap R S x)
     (hx : x = 0) : z = 0 := by
@@ -282,7 +282,7 @@ variable (M S)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (r : R), Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (Exists.{succ u1} (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)))))) M) (fun (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)))))) M) => Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) m) r) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (r : R), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) r) _inst_2))))) (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 _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 M)) (fun (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 M)) => Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (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))))) M)) m) r) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (r : R), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))))) (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 _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 M)) (fun (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 M)) => Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (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))))) M)) m) r) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_eq_zero_iff IsLocalization.map_eq_zero_iffₓ'. -/
 theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r = 0 :=
   by
@@ -330,7 +330,7 @@ theorem mk'_mul (x₁ x₂ : R) (y₁ y₂ : M) : mk' S (x₁ * x₂) (y₁ * y
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (OfNat.ofNat.{u1} (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)))))) M) 1 (OfNat.mk.{u1} (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)))))) M) 1 (One.one.{u1} (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)))))) M) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (OfNat.ofNat.{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 _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 M)) 1 (One.toOfNat1.{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 _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 M)) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (OfNat.ofNat.{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 _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 M)) 1 (One.toOfNat1.{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 _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 M)) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_one IsLocalization.mk'_oneₓ'. -/
 theorem mk'_one (x) : mk' S x (1 : M) = algebraMap R S x :=
   (toLocalizationMap M S).mk'_one _
@@ -340,7 +340,7 @@ theorem mk'_one (x) : mk' S x (1 : M) = algebraMap R S x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec IsLocalization.mk'_specₓ'. -/
 @[simp]
 theorem mk'_spec (x) (y : M) : mk' S x y * algebraMap R S y = algebraMap R S x :=
@@ -351,7 +351,7 @@ theorem mk'_spec (x) (y : M) : mk' S x y * algebraMap R S y = algebraMap R S x :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec' IsLocalization.mk'_spec'ₓ'. -/
 @[simp]
 theorem mk'_spec' (x) (y : M) : algebraMap R S y * mk' S x y = algebraMap R S x :=
@@ -362,7 +362,7 @@ theorem mk'_spec' (x) (y : M) : algebraMap R S y * mk' S x y = algebraMap R S x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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.hasMem.{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)))))) y M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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.hasMem.{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)))))) x M) y hy)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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)))))) y M), Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) y) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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 M) y hy)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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)))))) y M), Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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 M) y hy)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec_mk IsLocalization.mk'_spec_mkₓ'. -/
 @[simp]
 theorem mk'_spec_mk (x) (y : R) (hy : y ∈ M) :
@@ -374,7 +374,7 @@ theorem mk'_spec_mk (x) (y : R) (hy : y ∈ M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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.hasMem.{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)))))) y M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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.hasMem.{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)))))) x M) y hy))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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)))))) y M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) y) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) y) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) y) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) y) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) y) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) y) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) y) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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 M) y hy))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (hy : 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)))))) y M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) y) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) y) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x (Subtype.mk.{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 M) y hy))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec'_mk IsLocalization.mk'_spec'_mkₓ'. -/
 @[simp]
 theorem mk'_spec'_mk (x) (y : R) (hy : y ∈ M) :
@@ -388,7 +388,7 @@ variable {S}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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)))))) M} {z : S}, Iff (Eq.{succ u2} S z (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R 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R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {z : S}, Iff (Eq.{succ u1} S z (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S 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(NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {z : S}, Iff (Eq.{succ u1} S z (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x))
 Case conversion may be inaccurate. Consider using '#align is_localization.eq_mk'_iff_mul_eq IsLocalization.eq_mk'_iff_mul_eqₓ'. -/
 theorem eq_mk'_iff_mul_eq {x} {y : M} {z} :
     z = mk' S x y ↔ z * algebraMap R S y = algebraMap R S x :=
@@ -399,7 +399,7 @@ theorem eq_mk'_iff_mul_eq {x} {y : M} {z} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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)))))) M} {z : S}, Iff (Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, 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(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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {z : S}, Iff (Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {z : S}, Iff (Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq_mul IsLocalization.mk'_eq_iff_eq_mulₓ'. -/
 theorem mk'_eq_iff_eq_mul {x} {y : M} {z} :
     mk' S x y = z ↔ algebraMap R S x = z * algebraMap R S y :=
@@ -410,7 +410,7 @@ theorem mk'_eq_iff_eq_mul {x} {y : M} {z} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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)))))) M} {z₁ : S} {z₂ : S}, Iff (Eq.{succ u2} S (HAdd.hAdd.{u2, u2, u2} S S S (instHAdd.{u2} S (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z₁) z₂) (Eq.{succ u2} S (HAdd.hAdd.{u2, u2, u2} S S S (instHAdd.{u2} S (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) z₁ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S 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(Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x M))))) y))))
 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)))) (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => 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(MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {z₁ : S} {z₂ : S}, Iff (Eq.{succ u1} S (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) z₁) z₂) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Distrib.toAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonUnitalNonAssocSemiring.toDistrib.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R 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R _inst_1))))) M)) y)) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z₁ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S 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(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))))) M)) y))))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_add_eq_iff_add_mul_eq_mul IsLocalization.mk'_add_eq_iff_add_mul_eq_mulₓ'. -/
 theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
     mk' S x y + z₁ = z₂ ↔ algebraMap R S x + z₁ * algebraMap R S y = z₂ * algebraMap R S y := by
@@ -462,7 +462,7 @@ def uniqueOfZeroMem (h : (0 : R) ∈ M) : Unique S :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x₁ : R} {x₂ : R} {y₁ : 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)))))) M} {y₂ : 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)))))) M}, Iff (Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₁ y₁) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₂ y₂)) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) 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 but is expected to have type
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(MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₁) x₂)))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x₁ : R} {x₂ : R} {y₁ : 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 M)} {y₂ : 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 M)}, Iff (Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₁ y₁) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₂ y₂)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₂) x₁)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₂) x₁)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₁) x₂)))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq IsLocalization.mk'_eq_iff_eqₓ'. -/
 theorem mk'_eq_iff_eq {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (y₂ * x₁) = algebraMap R S (y₁ * x₂) :=
@@ -473,7 +473,7 @@ theorem mk'_eq_iff_eq {x₁ x₂} {y₁ y₂ : M} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x₁ : R} {x₂ : R} {y₁ : 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)))))) M} {y₂ : 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)))))) M}, Iff (Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₁ y₁) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₂ y₂)) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) 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 but is expected to have type
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(MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S 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(Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₁))))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x₁ : R} {x₂ : R} {y₁ : 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 M)} {y₂ : 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 M)}, Iff (Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₁ y₁) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x₂ y₂)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x₁ (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₂))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x₁ (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₂))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x₂ (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y₁))))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq' IsLocalization.mk'_eq_iff_eq'ₓ'. -/
 theorem mk'_eq_iff_eq' {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (x₁ * y₂) = algebraMap R S (x₂ * y₁) :=
@@ -484,7 +484,7 @@ theorem mk'_eq_iff_eq' {x₁ x₂} {y₁ y₂ : M} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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)))))) M} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)}, Iff (Membership.Mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) I) (Membership.Mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) I)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)}, Iff (Membership.mem.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.instSetLikeSubmodule.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) I) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.instSetLikeSubmodule.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) I)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)} {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)}, Iff (Membership.mem.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.instSetLikeSubmodule.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) I) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.instSetLikeSubmodule.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) I)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iffₓ'. -/
 theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R S x ∈ I :=
   by
@@ -549,7 +549,7 @@ variable [Algebra R P] [IsLocalization M P]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R P _inst_1 (CommSemiring.toSemiring.{u3} P _inst_4)] [_inst_7 : IsLocalization.{u1, u3} R _inst_1 M P _inst_4 _inst_6] {x : R} {y : R}, Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y)) (Eq.{succ u3} P (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (algebraMap.{u1, u3} R P _inst_1 (CommSemiring.toSemiring.{u3} P _inst_4) _inst_6) x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (algebraMap.{u1, u3} R P _inst_1 (CommSemiring.toSemiring.{u3} P _inst_4) _inst_6) y))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u2, u3} R _inst_1 M S _inst_2 _inst_3] [_inst_6 : Algebra.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4)] [_inst_7 : IsLocalization.{u2, u1} R _inst_1 M P _inst_4 _inst_6] {x : R} {y : R}, Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) y)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) (algebraMap.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4) _inst_6) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) (algebraMap.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4) _inst_6) y))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u2, u3} R _inst_1 M S _inst_2 _inst_3] [_inst_6 : Algebra.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4)] [_inst_7 : IsLocalization.{u2, u1} R _inst_1 M P _inst_4 _inst_6] {x : R} {y : R}, Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) y)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) (algebraMap.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4) _inst_6) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) (algebraMap.{u2, u1} R P _inst_1 (CommSemiring.toSemiring.{u1} P _inst_4) _inst_6) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.eq_iff_eq IsLocalization.eq_iff_eqₓ'. -/
 theorem eq_iff_eq {x y} :
     algebraMap R S x = algebraMap R S y ↔ algebraMap R P x = algebraMap R P y :=
@@ -629,7 +629,7 @@ end Ext
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (z : 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)))))) M), Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 y z)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x y) z)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (z : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 y z)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x y) z)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : R) (z : 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 M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 y z)) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x y) z)
 Case conversion may be inaccurate. Consider using '#align is_localization.mul_mk'_eq_mk'_of_mul IsLocalization.mul_mk'_eq_mk'_of_mulₓ'. -/
 theorem mul_mk'_eq_mk'_of_mul (x y : R) (z : M) :
     (algebraMap R S) x * mk' S y z = mk' S (x * y) z :=
@@ -640,7 +640,7 @@ theorem mul_mk'_eq_mk'_of_mul (x y : R) (z : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) y))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) y))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_mul_mk'_one IsLocalization.mk'_eq_mul_mk'_oneₓ'. -/
 theorem mk'_eq_mul_mk'_one (x : R) (y : M) : mk' S x y = (algebraMap R S) x * mk' S 1 y :=
   ((toLocalizationMap M S).mul_mk'_one_eq_mk' _ _).symm
@@ -650,7 +650,7 @@ theorem mk'_eq_mul_mk'_one (x : R) (y : M) : mk' S x y = (algebraMap R S) x * mk
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y) x) y) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y) x) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y) x) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_cancel_left IsLocalization.mk'_mul_cancel_leftₓ'. -/
 @[simp]
 theorem mk'_mul_cancel_left (x : R) (y : M) : mk' S (y * x : R) y = (algebraMap R S) x :=
@@ -661,7 +661,7 @@ theorem mk'_mul_cancel_left (x : R) (y : M) : mk' S (y * x : R) y = (algebraMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u2} S (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y)) y) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 M)), Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) x (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_cancel_right IsLocalization.mk'_mul_cancel_rightₓ'. -/
 theorem mk'_mul_cancel_right (x : R) (y : M) : mk' S (x * y) y = (algebraMap R S) x :=
   (toLocalizationMap M S).mk'_mul_cancel_right _ _
@@ -696,7 +696,7 @@ variable (M)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHom.comp.{u1, u2, u3} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] (j : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (RingHom.comp.{u1, u3, u2} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) j (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _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))))) M)) y))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] (j : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (RingHom.comp.{u1, u3, u2} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) j (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _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))))) M)) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.is_unit_comp IsLocalization.isUnit_compₓ'. -/
 theorem isUnit_comp (j : S →+* P) (y : M) : IsUnit (j.comp (algebraMap R S) y) :=
   (toLocalizationMap M S).isUnit_comp j.toMonoidHom _
@@ -708,7 +708,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g y)))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))}, (forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u3, u1} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) 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 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 Case conversion may be inaccurate. Consider using '#align is_localization.eq_of_eq IsLocalization.eq_of_eqₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g(M) ⊆ units P`, `f x = f y → g x = g y` for all `x y : R`. -/
@@ -739,7 +739,7 @@ theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (h : forall (y : 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 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 but is expected to have type
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R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) z₁)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R 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(SetLike.coe.{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))))) M)) y)) z₂))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] {g : RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} (h : forall (y : 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 M)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} 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M)) y)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} 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_inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x 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 Case conversion may be inaccurate. Consider using '#align is_localization.mul_add_inv_left IsLocalization.mul_add_inv_leftₓ'. -/
 theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (w z₁ z₂ : P) :
     w * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) h y)⁻¹ + z₁ = z₂ ↔ w + g y * z₁ = g y * z₂ :=
@@ -754,7 +754,7 @@ theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (
 lean 3 declaration is
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(coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M))))) (Prod.snd.{u1, u1} R (coeSort.{succ u1, 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 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _inst_1))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R 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(Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (NonUnitalNonAssocSemiring.toDistrib.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) _inst_4)))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) 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_inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) w')) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) v))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))) (z : S) (w : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (w' : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (v : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (HAdd.hAdd.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (instHAdd.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (Distrib.toAdd.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (NonUnitalNonAssocSemiring.toDistrib.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) _inst_4)))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) z) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S P (MulOneClass.toMul.{u1} S (MulZeroOneClass.toMulOneClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))))) (MulOneClass.toMul.{u2} P (MulZeroOneClass.toMulOneClass.{u2} P (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S P (MulZeroOneClass.toMulOneClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2)))) (MulZeroOneClass.toMulOneClass.{u2} P 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(MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4))))))) (Submonoid.LocalizationWithZeroMap.lift.{u3, u1, u2} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1) M S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2) P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4) (IsLocalization.toLocalizationWithZeroMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) (RingHom.toMonoidWithZeroHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) g) hg) z) w) w') v) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Prod.fst.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) M)) (Prod.snd.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u3} R (Monoid.toMulOneClass.{u3} R (CommMonoid.toMonoid.{u3} R (CommSemiring.toCommMonoid.{u3} R _inst_1))))) x M)) (Submonoid.LocalizationMap.sec.{u3, u1} R (CommSemiring.toCommMonoid.{u3} R _inst_1) M S (CommSemiring.toCommMonoid.{u1} S _inst_2) (IsLocalization.toLocalizationMap.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5) z)))) v))
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_spec_mul_add IsLocalization.lift_spec_mul_addₓ'. -/
 theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w' v) :
     ((toLocalizationWithZeroMap M S).lift g.toMonoidWithZeroHom hg) z * w + w' = v ↔
@@ -770,7 +770,7 @@ theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w'
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) -> (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (y : 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 M)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g (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))))) M)) y))) -> (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (y : 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 M)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g (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))))) M)) y))) -> (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))
 Case conversion may be inaccurate. Consider using '#align is_localization.lift IsLocalization.liftₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
@@ -798,7 +798,7 @@ variable {g : R →+* P} (hg : ∀ y : M, IsUnit (g y))
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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M) hg) y))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _inst_1))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R 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(CommSemiring.toSemiring.{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 _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MulOneClass.toMul.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M))) (MulOneClass.toMul.{u2} (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MonoidHom.monoidHomClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))))) (IsUnit.liftRight.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) P (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M) (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (MonoidHom.restrict.{u3, u2, u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) P (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instSubmonoidClassSubmonoidInstSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (RingHom.toMonoidHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) g) M) hg) y))))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} 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(CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MulOneClass.toMul.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M))) (MulOneClass.toMul.{u2} (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MonoidHom.monoidHomClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Units.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Monoid.toMulOneClass.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M)) (Units.instMulOneClassUnits.{u2} P (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))))) (IsUnit.liftRight.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) P (Submonoid.toMonoid.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M) (MonoidWithZero.toMonoid.{u2} P (Semiring.toMonoidWithZero.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (MonoidHom.restrict.{u3, u2, u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) P (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instSubmonoidClassSubmonoidInstSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (RingHom.toMonoidHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) g) M) hg) y))))
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk' IsLocalization.lift_mk'ₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
@@ -812,7 +812,7 @@ theorem lift_mk' (x y) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 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 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} 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(Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P 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(CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) v) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P 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(MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) P ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) v))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} 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 Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk'_spec IsLocalization.lift_mk'_specₓ'. -/
 theorem lift_mk'_spec (x v) (y : M) : lift hg (mk' S x y) = v ↔ g x = g y * v :=
   (toLocalizationMap M S).lift_mk'_spec _ _ _ _
@@ -822,7 +822,7 @@ theorem lift_mk'_spec (x v) (y : M) : lift hg (mk' S x y) = v ↔ g x = g y * v
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) (x : R), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => S -> P) (RingHom.hasCoeToFun.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (IsLocalization.lift.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (MonoidWithZero.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, 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(Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (RingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) P (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (RingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) P (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) P (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u1, u3} (RingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) P (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u1, u3} (RingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) P (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) P (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) P (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) (IsLocalization.lift.{u2, u1, u3} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g x)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (MonoidWithZero.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y))) (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => P) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (RingHom.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) P (Semiring.toNonAssocSemiring.{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) _inst_2)) 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R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g x)
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_eq IsLocalization.lift_eqₓ'. -/
 @[simp]
 theorem lift_eq (x : R) : lift hg ((algebraMap R S) x) = g x :=
@@ -833,7 +833,7 @@ theorem lift_eq (x : R) : lift hg ((algebraMap R S) x) = g x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 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R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (SetLike.hasMem.{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)))))) x M))))) (Prod.snd.{u1, u1} R (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)))))) M) x)))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Subtype.val.{succ u3} R (fun (x : R) => Membership.mem.{u3, u3} R (Set.{u3} R) (Set.instMembershipSet.{u3} R) x (SetLike.coe.{u3, 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M))} {y : Prod.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M))}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (Prod.fst.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, 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(NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{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 _inst_1)))))) x M)) x))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (Prod.fst.{u3, u3} R (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 _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 _inst_1))))) R 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(Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g 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(Prod.snd.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) y)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (HMul.hMul.{u3, u3, u3} R R R (instHMul.{u3} R (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Prod.fst.{u3, u3} R (Subtype.{succ u3} R 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(Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) (Prod.snd.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) y)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (HMul.hMul.{u3, u3, u3} R R R (instHMul.{u3} R (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Prod.fst.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) y) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) (Prod.snd.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) x)))))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))) {x : Prod.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M))} {y : Prod.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M))}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (Prod.fst.{u3, u3} R (Subtype.{succ u3} R (fun (x : R) => Membership.mem.{u3, 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(NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{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 _inst_1)))))) x M)) x))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S 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(Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} S P (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (IsLocalization.mk'.{u3, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 (Prod.fst.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) x) (Prod.snd.{u3, u3} R (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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)) x))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S P 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 Case conversion may be inaccurate. Consider using '#align is_localization.lift_eq_iff IsLocalization.lift_eq_iffₓ'. -/
 theorem lift_eq_iff {x y : R × M} :
     lift hg (mk' S x.1 x.2) = lift hg (mk' S y.1 y.2) ↔ g (x.1 * y.2) = g (y.1 * x.2) :=
@@ -844,7 +844,7 @@ theorem lift_eq_iff {x y : R × M} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 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(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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))), Eq.{max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHom.comp.{u1, u2, u3} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (IsLocalization.lift.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) g
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))), Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHom.comp.{u3, u1, u2} R S P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (algebraMap.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) g
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))), Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHom.comp.{u3, u1, u2} R S P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (IsLocalization.lift.{u3, u1, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) (algebraMap.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) g
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_comp IsLocalization.lift_compₓ'. -/
 @[simp]
 theorem lift_comp : (lift hg).comp (algebraMap R S) = g :=
@@ -906,7 +906,7 @@ theorem algHom_subsingleton [Algebra R P] : Subsingleton (S →ₐ[R] P) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : S -> P) (k : S -> P), (Eq.{succ u3} P (j (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (OfNat.ofNat.{u3} P 1 (OfNat.mk.{u3} P 1 (One.one.{u3} P (AddMonoidWithOne.toOne.{u3} P (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} P (NonAssocSemiring.toAddCommMonoidWithOne.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) -> (Eq.{succ u3} P (k (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (OfNat.ofNat.{u3} P 1 (OfNat.mk.{u3} P 1 (One.one.{u3} P (AddMonoidWithOne.toOne.{u3} P (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} P (NonAssocSemiring.toAddCommMonoidWithOne.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) -> (forall (a : S) (b : S), Eq.{succ u3} P (j (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) (j a) (j b))) -> (forall (a : S) (b : S), Eq.{succ u3} P (k (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) (k a) (k b))) -> (forall (a : R), Eq.{succ u3} P (j (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a)) (k (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a))) -> (Eq.{max (succ u2) (succ u3)} (S -> P) j k)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : S -> P) (k : S -> P), (Eq.{succ u3} P (j (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> (Eq.{succ u3} P (k (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> (forall (a : S) (b : S), Eq.{succ u3} P (j (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (j a) (j b))) -> (forall (a : S) (b : S), Eq.{succ u3} P (k (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (k a) (k b))) -> (forall (a : R), Eq.{succ u3} P (j (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a)) (k (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a))) -> (Eq.{max (succ u2) (succ u3)} (S -> P) j k)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : S -> P) (k : S -> P), (Eq.{succ u3} P (j (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> (Eq.{succ u3} P (k (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> (forall (a : S) (b : S), Eq.{succ u3} P (j (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (j a) (j b))) -> (forall (a : S) (b : S), Eq.{succ u3} P (k (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (k a) (k b))) -> (forall (a : R), Eq.{succ u3} P (j (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a)) (k (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a))) -> (Eq.{max (succ u2) (succ u3)} (S -> P) j k)
 Case conversion may be inaccurate. Consider using '#align is_localization.ext IsLocalization.extₓ'. -/
 /-- To show `j` and `k` agree on the whole localization, it suffices to show they agree
 on the image of the base ring, if they preserve `1` and `*`. -/
@@ -922,7 +922,7 @@ variable {M}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))) {j : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}, (forall (x : R), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => S -> P) (RingHom.hasCoeToFun.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) j (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x)) -> (Eq.{max (succ u2) (succ u3)} (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (IsLocalization.lift.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) j)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) y))) {j : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))}, (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P 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P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g x)) -> (Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (IsLocalization.lift.{u1, u3, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) j)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) y))) {j : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))}, (forall (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) j (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g x)) -> (Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (IsLocalization.lift.{u1, u3, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) j)
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_unique IsLocalization.lift_uniqueₓ'. -/
 theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) : lift hg = j :=
   RingHom.ext <|
@@ -935,7 +935,7 @@ theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : S), Eq.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (IsLocalization.lift.{u1, u2, u2} R _inst_1 M S _inst_2 _inst_3 S _inst_2 _inst_5 (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (IsLocalization.map_units.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) x
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.lift.{u1, u2, u2} R _inst_1 M S _inst_2 _inst_3 S _inst_2 _inst_5 (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (IsLocalization.map_units.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) x
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (IsLocalization.lift.{u1, u2, u2} R _inst_1 M S _inst_2 _inst_3 S _inst_2 _inst_5 (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (IsLocalization.map_units.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5)) x) x
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_id IsLocalization.lift_idₓ'. -/
 @[simp]
 theorem lift_id (x) : lift (map_units S : ∀ y : M, IsUnit _) x = x :=
@@ -946,7 +946,7 @@ theorem lift_id (x) : lift (map_units S : ∀ y : M, IsUnit _) x = x :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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 but is expected to have type
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(RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) (Prod.snd.{u1, u1} R (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 M)) x)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Prod.fst.{u1, u1} R (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 M)) x))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) y))), Iff (Function.Surjective.{succ u3, succ u2} S P (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S 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P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (Prod.fst.{u1, u1} R (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 M)) x))))
 Case conversion may be inaccurate. Consider using '#align is_localization.lift_surjective_iff IsLocalization.lift_surjective_iffₓ'. -/
 theorem lift_surjective_iff :
     Surjective (lift hg : S → P) ↔ ∀ v : P, ∃ x : R × M, v * g x.2 = g x.1 :=
@@ -957,7 +957,7 @@ theorem lift_surjective_iff :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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)))))) M), IsUnit.{u3} P (MonoidWithZero.toMonoid.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y))), Iff (Function.Injective.{succ u2, succ u3} S P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => S -> P) (RingHom.hasCoeToFun.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (IsLocalization.lift.{u1, u2, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg))) (forall (x : R) (y : R), Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) y)) (Eq.{succ u3} P (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g y)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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))))) M)) y))), Iff (Function.Injective.{succ u3, succ u2} S P (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u3, u2} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) (IsLocalization.lift.{u1, u3, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg))) (forall (x : R) (y : R), Iff (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) y)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g y)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) (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 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 Case conversion may be inaccurate. Consider using '#align is_localization.lift_injective_iff IsLocalization.lift_injective_iffₓ'. -/
 theorem lift_injective_iff :
     Injective (lift hg : S → P) ↔ ∀ x y, algebraMap R S x = algebraMap R S y ↔ g x = g y :=
@@ -996,7 +996,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => P -> Q) (RingHom.hasCoeToFun.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) => Q) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) Q (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (algebraMap.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => Q) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u3 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((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) Q (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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(Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u1, u4} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (algebraMap.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_eq IsLocalization.map_eqₓ'. -/
 theorem map_eq (x) : map Q g hy ((algebraMap R S) x) = algebraMap P Q (g x) :=
   lift_eq (fun y => map_units _ ⟨g y, hy y.2⟩) x
@@ -1017,7 +1017,7 @@ theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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 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_inst_1)))))) x M) y) (Subtype.property.{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.hasMem.{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)))))) x M) y))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u4, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u4, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Preorder.toLE.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))))) M (Submonoid.comap.{u4, u1, max u4 u1} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u4, u2, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) x) _inst_4 T Q _inst_6 _inst_7 _inst_8 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) 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(Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y)) (hy (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y))))
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u4, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u4, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Preorder.toLE.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))))) M (Submonoid.comap.{u4, u1, max u4 u1} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u4, u2, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (IsLocalization.mk'.{u4, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) _inst_4 T Q _inst_6 _inst_7 _inst_8 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) _inst_4))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) _inst_4))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) x) _inst_4)))))) x_1 T) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y)) (hy (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y))))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_mk' IsLocalization.map_mk'ₓ'. -/
 theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.2⟩ :=
   @Submonoid.LocalizationMap.map_mk' _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom _
@@ -1028,7 +1028,7 @@ theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u1, u1} R R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toMonoidHomClass.{u1, u1, u1} (RingHom.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ringHomClass.{u1, u1} R R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M)) (le_refl.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) M)), Eq.{succ u2} S (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => S -> S) (RingHom.hasCoeToFun.{u2, u2} S S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (IsLocalization.map.{u1, u2, u1, u2} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) h) z) z
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u2, u2} R R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toMonoidHomClass.{u2, u2, u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M)) (le_refl.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))) M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (IsLocalization.map.{u2, u1, u2, u1} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) h) z) z
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u2, u2} R R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toMonoidHomClass.{u2, u2, u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M)) (le_refl.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))) M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (IsLocalization.map.{u2, u1, u2, u1} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) h) z) z
 Case conversion may be inaccurate. Consider using '#align is_localization.map_id IsLocalization.map_idₓ'. -/
 @[simp]
 theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
@@ -1040,7 +1040,7 @@ theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))), (forall (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) j (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => P -> Q) (RingHom.hasCoeToFun.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x))) -> (Eq.{max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u4}} [_inst_2 : CommSemiring.{u4} S] [_inst_3 : Algebra.{u2, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u2, u4} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u1, max u2 u1} R P (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))), (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (algebraMap.{u2, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) j (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} 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x)) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q 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(CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))) -> (Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (IsLocalization.map.{u2, u4, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u4}} [_inst_2 : CommSemiring.{u4} S] [_inst_3 : Algebra.{u2, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u2, u4} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) M (Submonoid.comap.{u2, u1, max u2 u1} R P (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))), (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S 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S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u4, u2, u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (algebraMap.{u2, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : P) => Q) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P Q (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u1, u3} P Q (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (algebraMap.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6) _inst_7) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))) -> (Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (IsLocalization.map.{u2, u4, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
 Case conversion may be inaccurate. Consider using '#align is_localization.map_unique IsLocalization.map_uniqueₓ'. -/
 theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algebraMap P Q (g x)) :
     map Q g hy = j :=
@@ -1051,7 +1051,7 @@ theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algeb
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toLE.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)), Eq.{max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (RingHom.comp.{u2, u4, u6} S Q W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10)) (IsLocalization.map.{u3, u4, u5, u6} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u2, u5, u6} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u3, u5} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) l g) (fun (x : R) (hx : 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.hasMem.{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)))))) x M) => hl (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (FunLike.hasCoeToFun.{succ (max u1 u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u2} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)), Eq.{max (succ u3) (succ u5)} (RingHom.{u3, u5} S W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHom.comp.{u3, u2, u5} S Q W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (IsLocalization.map.{u4, u2, u6, u5} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u3, u4, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u3, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u2} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)), Eq.{max (succ u3) (succ u5)} (RingHom.{u3, u5} S W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHom.comp.{u3, u2, u5} S Q W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (IsLocalization.map.{u4, u2, u6, u5} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u3, u4, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u3, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx)))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_comp_map IsLocalization.map_comp_mapₓ'. -/
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
@@ -1067,7 +1067,7 @@ theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSe
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toLE.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)) (x : S), Eq.{succ u6} W (coeFn.{max (succ u4) (succ u6), max (succ u4) (succ u6)} (RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (fun (_x : RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) => Q -> W) (RingHom.hasCoeToFun.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (IsLocalization.map.{u3, u4, u5, u6} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (coeFn.{max (succ u2) (succ u6), max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (fun (_x : RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) => S -> W) (RingHom.hasCoeToFun.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (IsLocalization.map.{u1, u2, u5, u6} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u3, u5} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (FunLike.hasCoeToFun.{succ (max u1 u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u3} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)) (x : S), Eq.{succ u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) => W) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (a : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) a) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u1, u2, u4, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (FunLike.coe.{max (succ u5) (succ u3), succ u3, succ u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) => W) _x) (MulHomClass.toFunLike.{max u5 u3, u3, u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) W (NonUnitalNonAssocSemiring.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6)))) (NonUnitalNonAssocSemiring.toMul.{u5} W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))) (NonUnitalRingHomClass.toMulHomClass.{max u5 u3, u3, u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHomClass.toNonUnitalRingHomClass.{max u5 u3, u3, u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (RingHom.instRingHomClassRingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u4, u3, u6, u5} P _inst_4 T ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u1, u2, u4, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (FunLike.coe.{max (succ u5) (succ u2), succ u2, succ u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => W) _x) (MulHomClass.toFunLike.{max u5 u2, u2, u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u5} W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))) (NonUnitalRingHomClass.toMulHomClass.{max u5 u2, u2, u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHomClass.toNonUnitalRingHomClass.{max u5 u2, u2, u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (RingHom.instRingHomClassRingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u1, u2, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx))) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u3} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)) (x : S), Eq.{succ u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) => W) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (a : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) a) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u1, u2, u4, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) (FunLike.coe.{max (succ u5) (succ u3), succ u3, succ u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) => W) _x) (MulHomClass.toFunLike.{max u5 u3, u3, u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) 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_inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHomClass.toNonUnitalRingHomClass.{max u5 u3, u3, u5} (RingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (RingHom.instRingHomClassRingHom.{u3, u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) W (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u4, u3, u6, u5} P _inst_4 T ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Q (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6)))))) (IsLocalization.map.{u1, u2, u4, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x)) 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} W (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHomClass.toNonUnitalRingHomClass.{max u5 u2, u2, u5} (RingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (RingHom.instRingHomClassRingHom.{u2, u5} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u1, u2, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx))) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.map_map IsLocalization.map_mapₓ'. -/
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
@@ -1081,7 +1081,7 @@ theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemirin
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (SMul.smul.{u1, u2} R S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3))))) z x)) (SMul.smul.{u3, u4} P Q (SMulZeroClass.toHasSmul.{u3, u4} P Q (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} P Q (MulZeroClass.toHasZero.{u3} P (MulZeroOneClass.toMulZeroClass.{u3} P (MonoidWithZero.toMulZeroOneClass.{u3} P (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} P Q (Semiring.toMonoidWithZero.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (AddZeroClass.toHasZero.{u4} Q (AddMonoid.toAddZeroClass.{u4} Q (AddCommMonoid.toAddMonoid.{u4} Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))) (Module.toMulActionWithZero.{u3, u4} P Q (CommSemiring.toSemiring.{u3} P _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (Algebra.toModule.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7))))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g z) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (HSMul.hSMul.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (instHSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (Algebra.toSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_4 (CommSemiring.toSemiring.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6) _inst_7)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g z) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (HSMul.hSMul.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (instHSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) (Algebra.toSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_4 (CommSemiring.toSemiring.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) x) _inst_6) _inst_7)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g z) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_smul IsLocalization.map_smulₓ'. -/
 theorem map_smul (x : S) (z : R) : map Q g hy (z • x : S) = g z • map Q g hy x := by
   rw [Algebra.smul_def, Algebra.smul_def, RingHom.map_mul, map_eq]
@@ -1143,7 +1143,7 @@ theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T) (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingEquiv.{u2, u4} S Q (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasMul.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))) (Distrib.toHasAdd.{u4} Q 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 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R 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(NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (RingEquivClass.toMulEquivClass.{max u1 u2, u1, u2} (RingEquiv.{u1, u2} S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Distrib.toAdd.{u2} Q (NonUnitalNonAssocSemiring.toDistrib.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u2} Q (NonUnitalNonAssocSemiring.toDistrib.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))))) (RingEquiv.instRingEquivClassRingEquiv.{u1, u2} S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Distrib.toAdd.{u2} Q (NonUnitalNonAssocSemiring.toDistrib.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))))))) (IsLocalization.ringEquivOfRingEquiv.{u4, u1, u3, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 j H) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))) P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u3, u2} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))))) (algebraMap.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6) _inst_7) (FunLike.coe.{max (succ u4) (succ u3), succ u4, 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(NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))))) j x))
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R 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(NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))))) j x))
 Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eqₓ'. -/
 @[simp]
 theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x) :
@@ -1155,7 +1155,7 @@ theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T) (x : R) (y : 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)))))) M), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingEquiv.{u2, u4} S Q 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(NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasMul.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))) (Distrib.toHasAdd.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.ringEquivOfRingEquiv.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 j H) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u3, u4} P _inst_4 T Q _inst_6 _inst_7 _inst_8 (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R 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(SetLike.hasMem.{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)))))) x M))))) y) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} 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_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)))))) x M) y))))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y)) T H)])))
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u4, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] [_inst_7 : Algebra.{u3, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u2} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u4, u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u4, u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T) (x : R) (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M)), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : S) => Q) (IsLocalization.mk'.{u4, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) 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(NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u2} Q (NonUnitalNonAssocSemiring.toDistrib.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6))))) (RingEquiv.instRingEquivClassRingEquiv.{u1, u2} S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Distrib.toAdd.{u2} Q 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R (fun (a : R) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : R) => P) a) (EmbeddingLike.toFunLike.{max (succ u4) (succ u3), succ u4, succ u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (MulEquivClass.toEquivLike.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingEquivClass.toMulEquivClass.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))))) j) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) M)) y) (SetLike.coe.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{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 _inst_1))))) M) (Subtype.property.{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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) x M) y)) T H)])))
 Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_mk' IsLocalization.ringEquivOfRingEquiv_mk'ₓ'. -/
 theorem ringEquivOfRingEquiv_mk' {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x : R) (y : M) :
     ringEquivOfRingEquiv S Q j H (mk' S x y) =
@@ -1601,7 +1601,7 @@ theorem toLocalizationMap_eq_monoidOf : toLocalizationMap M (Localization M) = m
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (fun (_x : MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) => R -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (MonoidHom.hasCoeToFun.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (Submonoid.LocalizationMap.toMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (fun (_x : RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) => R -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (RingHom.hasCoeToFun.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M))) (MonoidHom.monoidHomClass.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))))) (Submonoid.LocalizationMap.toMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M))) (MonoidHom.monoidHomClass.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommMonoid.toMonoid.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)))))) (Submonoid.LocalizationMap.toMap.{u1, u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommMonoidLocalization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.monoidOf.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align localization.monoid_of_eq_algebra_map Localization.monoidOf_eq_algebraMapₓ'. -/
 theorem monoidOf_eq_algebraMap (x) : (monoidOf M).toMap x = algebraMap R (Localization M) x :=
   rfl
@@ -1611,7 +1611,7 @@ theorem monoidOf_eq_algebraMap (x) : (monoidOf M).toMap x = algebraMap R (Locali
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (fun (_x : RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) => R -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (RingHom.hasCoeToFun.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (x : R), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) x M)) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u1, u1} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align localization.mk_one_eq_algebra_map Localization.mk_one_eq_algebraMapₓ'. -/
 theorem mk_one_eq_algebraMap (x) : mk x 1 = algebraMap R (Localization M) x :=
   rfl
@@ -1642,7 +1642,7 @@ theorem mk_eq_mk' : (mk : R → M → Localization M) = IsLocalization.mk' (Loca
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : 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_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1)] (m : A), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => A -> R) (RingHom.hasCoeToFun.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (algebraMap.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6) m) (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M) (Submonoid.one.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M))))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (fun (_x : RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) => A -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (RingHom.hasCoeToFun.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)))) (algebraMap.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_5 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (Localization.algebra.{u1, u2} R _inst_1 M A _inst_5 _inst_6)) m)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : 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_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1)] (m : A), Eq.{succ u1} (Localization.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) _inst_1) M) (Localization.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) _inst_1) M (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (algebraMap.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6) m) (OfNat.ofNat.{u1} (Subtype.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (fun (x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (fun (x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) _inst_1))))) x M)) (Submonoid.one.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => R) m) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : A) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_5 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u2} R _inst_1 M A _inst_5 _inst_6)) m)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : 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_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1)] (m : A), Eq.{succ u1} (Localization.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1) M) (Localization.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1) M (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u1} A R (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (algebraMap.{u2, u1} A R _inst_5 (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6) m) (OfNat.ofNat.{u1} (Subtype.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (fun (x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1))))) x M)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (fun (x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (CommSemiring.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) _inst_1))))) x M)) (Submonoid.one.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => R) m) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)))) A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))) (RingHom.instRingHomClassRingHom.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)) (Semiring.toNonAssocSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M))))))) (algebraMap.{u2, u1} A (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_5 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u2} R _inst_1 M A _inst_5 _inst_6)) m)
 Case conversion may be inaccurate. Consider using '#align localization.mk_algebra_map Localization.mk_algebraMapₓ'. -/
 theorem mk_algebraMap {A : Type _} [CommSemiring A] [Algebra A R] (m : A) :
     mk (algebraMap A R m) 1 = algebraMap A (Localization M) m := by
@@ -1831,7 +1831,7 @@ variable {R M} (S) {K : Type _} [IsLocalization M S]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {x : R}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] {x : R}, (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))))) (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] {x : R}, (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))) (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iffₓ'. -/
 theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R S x = 0 ↔ x = 0 :=
   by
@@ -1847,7 +1847,7 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Function.Injective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3)))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Function.Injective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align is_localization.injective IsLocalization.injectiveₓ'. -/
 protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraMap R S) :=
   by
@@ -1860,7 +1860,7 @@ protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraM
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {x : R}, (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (forall {x : R}, (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) x (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (forall {x : R}, (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) x (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{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_2)))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.to_map_ne_zero_of_mem_non_zero_divisors IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisorsₓ'. -/
 protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M ≤ nonZeroDivisors R)
     {x : R} (hx : x ∈ nonZeroDivisors R) : algebraMap R S x ≠ 0 :=
@@ -1903,7 +1903,7 @@ variable (S M) (Q : Type _) [CommRing Q] {g : R →+* P} [Algebra P Q]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] (Q : Type.{u4}) [_inst_6 : CommRing.{u4} Q] {g : RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u4} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (Ring.toSemiring.{u4} Q (CommRing.toRing.{u4} Q _inst_6))], (Function.Injective.{succ u1, succ u3} R P (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (fun (_x : RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u4} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7], Function.Injective.{succ u2, succ u4} S Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (IsLocalization.map.{u1, u2, u3, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] (Q : Type.{u2}) [_inst_6 : CommRing.{u2} Q] {g : RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u2} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (Ring.toSemiring.{u2} Q (CommRing.toRing.{u2} Q _inst_6))], (Function.Injective.{succ u4, succ u3} R P (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u2} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7], Function.Injective.{succ u1, succ u2} S Q (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))) (RingHom.instRingHomClassRingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))))) (IsLocalization.map.{u4, u1, u3, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{max u4 u3, u3, u4} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] (Q : Type.{u2}) [_inst_6 : CommRing.{u2} Q] {g : RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u2} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (Ring.toSemiring.{u2} Q (CommRing.toRing.{u2} Q _inst_6))], (Function.Injective.{succ u4, succ u3} R P (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u2} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7], Function.Injective.{succ u1, succ u2} S Q (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Q) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))) (RingHom.instRingHomClassRingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))))) (IsLocalization.map.{u4, u1, u3, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{max u4 u3, u3, u4} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injectiveₓ'. -/
 /-- Injectivity of a map descends to the map induced on localizations. -/
 theorem map_injective_of_injective (hg : Function.Injective g)
@@ -1997,7 +1997,7 @@ open IsLocalization
 lean 3 declaration is
   forall {R : Type.{u1}} {Rₘ : Type.{u2}} [_inst_5 : CommRing.{u1} R] [_inst_6 : CommRing.{u2} Rₘ] {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_5)))))}, (Not (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_5)))))) (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_5)))))) 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_5))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))))) M)) -> (IsField.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) -> (forall [_inst_7 : Algebra.{u1, u2} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u1, succ u2} R Rₘ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) (fun (_x : RingHom.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) => R -> Rₘ) (RingHom.hasCoeToFun.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) (algebraMap.{u1, u2} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)) _inst_7)))
 but is expected to have type
-  forall {R : Type.{u2}} {Rₘ : Type.{u1}} [_inst_5 : CommRing.{u2} R] [_inst_6 : CommRing.{u1} Rₘ] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))}, (Not (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) M)) -> (IsField.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5))) -> (forall [_inst_7 : Algebra.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} R Rₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Rₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))))))) (algebraMap.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)) _inst_7)))
+  forall {R : Type.{u2}} {Rₘ : Type.{u1}} [_inst_5 : CommRing.{u2} R] [_inst_6 : CommRing.{u1} Rₘ] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))}, (Not (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) M)) -> (IsField.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5))) -> (forall [_inst_7 : Algebra.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} R Rₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Rₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))))))) (algebraMap.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align is_field.localization_map_bijective IsField.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommRing Rₘ]
@@ -2016,7 +2016,7 @@ theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommR
 lean 3 declaration is
   forall {K : Type.{u1}} {Kₘ : Type.{u2}} [_inst_5 : Field.{u1} K] [_inst_6 : CommRing.{u2} Kₘ] {M : Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))}, (Not (Membership.Mem.{u1, u1} K (Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))) K (Submonoid.setLike.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))))))) M)) -> (forall [_inst_7 : Algebra.{u1, u2} K Kₘ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u1, u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u2} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u1, succ u2} K Kₘ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) (fun (_x : RingHom.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) => K -> Kₘ) (RingHom.hasCoeToFun.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) (algebraMap.{u1, u2} K Kₘ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)) _inst_7)))
 but is expected to have type
-  forall {K : Type.{u2}} {Kₘ : Type.{u1}} [_inst_5 : Field.{u2} K] [_inst_6 : CommRing.{u1} Kₘ] {M : Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))}, (Not (Membership.mem.{u2, u2} K (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))) K (Submonoid.instSetLikeSubmonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))))) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) M)) -> (forall [_inst_7 : Algebra.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} K Kₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : K) => Kₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) (NonUnitalNonAssocSemiring.toMul.{u1} Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))))))) (algebraMap.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)) _inst_7)))
+  forall {K : Type.{u2}} {Kₘ : Type.{u1}} [_inst_5 : Field.{u2} K] [_inst_6 : CommRing.{u1} Kₘ] {M : Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))}, (Not (Membership.mem.{u2, u2} K (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))) K (Submonoid.instSetLikeSubmonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))))) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) M)) -> (forall [_inst_7 : Algebra.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} K Kₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Kₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) (NonUnitalNonAssocSemiring.toMul.{u1} Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))))))) (algebraMap.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align field.localization_map_bijective Field.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem Field.localization_map_bijective {K Kₘ : Type _} [Field K] [CommRing Kₘ] {M : Submonoid K}
@@ -2071,7 +2071,7 @@ include S
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Sₘ : Type.{u3}) [_inst_6 : CommRing.{u3} Sₘ] [_inst_9 : Algebra.{u2, u3} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u3} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u1, u2, u3} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} S Sₘ (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u3} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (Algebra.toModule.{u2, u3} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u3} R Sₘ (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Sₘ (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.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Sₘ (AddMonoid.toAddZeroClass.{u3} Sₘ (AddCommMonoid.toAddMonoid.{u3} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u3} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (Algebra.toModule.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)))))] (y : 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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Sₘ _inst_6)))) => R -> Sₘ) (RingHom.hasCoeToFun.{u1, u3} R Sₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) (algebraMap.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12) ((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 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(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))))))) M) 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))))))) M) 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 M))))) y))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] (Sₘ : Type.{u1}) [_inst_6 : CommRing.{u1} Sₘ] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u2, u3, u1} R S Sₘ (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3) (Algebra.toSMul.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_12)] (y : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) x M)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 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(CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_12) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] (Sₘ : Type.{u1}) [_inst_6 : CommRing.{u1} Sₘ] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u2, u3, u1} R S Sₘ (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3) (Algebra.toSMul.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_12)] (y : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))))) x M)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y)) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Sₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_12) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y))
 Case conversion may be inaccurate. Consider using '#align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoidₓ'. -/
 theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R Sₘ y) :=
   by
@@ -2083,7 +2083,7 @@ theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R S
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : R) (y : 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)))))) 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))))))) M) 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))))))) M) 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))))))) M) 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))))))) M) 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 M))))) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M y)))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u4, u2, u3} R Rₘ Sₘ (Algebra.toSMul.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u4, u1, u3} R S Sₘ (Algebra.toSMul.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] (x : R) (y : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))))) x M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))))) (algebraMap.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))))))) x_1 (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (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 (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) M)) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u4} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M y)))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u4, u2, u3} R Rₘ Sₘ (Algebra.toSMul.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u4, u1, u3} R S Sₘ (Algebra.toSMul.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] (x : R) (y : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))))) x M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))))) (algebraMap.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u1, u3} ((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_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) (Semiring.toNonAssocSemiring.{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_2))))))) x_1 (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (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 (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) M)) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u4} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M y)))
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_mk' IsLocalization.algebraMap_mk'ₓ'. -/
 @[simp]
 theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
@@ -2126,7 +2126,7 @@ theorem IsLocalization.algebraMap_eq_map_map_submonoid :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : Rₘ), Eq.{succ u4} Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))) x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u4} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u3, u4} R Rₘ Sₘ (Algebra.toSMul.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u4} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)] (x : Rₘ), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (IsLocalization.map.{u2, u3, u1, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3))])) x)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u4} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u3, u4} R Rₘ Sₘ (Algebra.toSMul.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u4} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)] (x : Rₘ), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (IsLocalization.map.{u2, u3, u1, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3))])) x)
 Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
@@ -2165,7 +2165,7 @@ variable (Rₘ Sₘ)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u3, succ u4} Rₘ Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) (localizationAlgebra.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))} {S : Type.{u3}} [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u1}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u1} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u4, succ u3} R S (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (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} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))))) (algebraMap.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u2, succ u1} Rₘ Sₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) (localizationAlgebra.{u4, u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))} {S : Type.{u3}} [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u1}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u1} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u4, succ u3} R S (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (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} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))))) (algebraMap.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u2, succ u1} Rₘ Sₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) (localizationAlgebra.{u4, u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
 Case conversion may be inaccurate. Consider using '#align localization_algebra_injective localizationAlgebra_injectiveₓ'. -/
 /-- Injectivity of the underlying `algebra_map` descends to the algebra induced by localization. -/
 theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)) :

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

@@ -291,8 +291,8 @@ theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r =
   · obtain ⟨m, hm⟩ := (IsLocalization.eq_iff_exists M S).mp ((algebraMap R S).map_zero.trans h.symm)
     exact ⟨m, by simpa using hm.symm⟩
   · rintro ⟨m, hm⟩
-    rw [← (IsLocalization.map_units S m).mul_right_inj, mul_zero, ← RingHom.map_mul, hm,
-      RingHom.map_zero]
+    rw [← (IsLocalization.map_units S m).mul_right_inj, MulZeroClass.mul_zero, ← RingHom.map_mul,
+      hm, RingHom.map_zero]
 #align is_localization.map_eq_zero_iff IsLocalization.map_eq_zero_iff
 
 variable {M}
@@ -515,7 +515,7 @@ but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : 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 M)), Iff (Eq.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x s) (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))))) (Exists.{succ 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 _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 M)) (fun (m : 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 M)) => Eq.{succ u2} R (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) m) x) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_zero_iff IsLocalization.mk'_eq_zero_iffₓ'. -/
 theorem mk'_eq_zero_iff (x : R) (s : M) : mk' S x s = 0 ↔ ∃ m : M, ↑m * x = 0 := by
-  rw [← (map_units S s).mul_left_inj, mk'_spec, zero_mul, map_eq_zero_iff M]
+  rw [← (map_units S s).mul_left_inj, mk'_spec, MulZeroClass.zero_mul, map_eq_zero_iff M]
 #align is_localization.mk'_eq_zero_iff IsLocalization.mk'_eq_zero_iff
 
 /- warning: is_localization.mk'_zero -> IsLocalization.mk'_zero is a dubious translation:
@@ -526,7 +526,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align is_localization.mk'_zero IsLocalization.mk'_zeroₓ'. -/
 @[simp]
 theorem mk'_zero (s : M) : IsLocalization.mk' S 0 s = 0 := by
-  rw [eq_comm, IsLocalization.eq_mk'_iff_mul_eq, zero_mul, map_zero]
+  rw [eq_comm, IsLocalization.eq_mk'_iff_mul_eq, MulZeroClass.zero_mul, map_zero]
 #align is_localization.mk'_zero IsLocalization.mk'_zero
 
 /- warning: is_localization.ne_zero_of_mk'_ne_zero -> IsLocalization.ne_zero_of_mk'_ne_zero is a dubious translation:
@@ -1337,7 +1337,7 @@ theorem nonZeroDivisors_le_comap [IsLocalization M S] :
   rw [← @mk'_one R _ M, ← mk'_mul, ← (algebraMap R S).map_zero, ← @mk'_one R _ M,
     IsLocalization.eq] at e
   obtain ⟨c, e⟩ := e
-  rw [mul_zero, mul_zero, Submonoid.coe_one, one_mul, ← mul_assoc] at e
+  rw [MulZeroClass.mul_zero, MulZeroClass.mul_zero, Submonoid.coe_one, one_mul, ← mul_assoc] at e
   rw [mk'_eq_zero_iff]
   exact ⟨c, ha _ e⟩
 #align is_localization.non_zero_divisors_le_comap IsLocalization.nonZeroDivisors_le_comap
@@ -1838,7 +1838,7 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
   rw [← (algebraMap R S).map_zero]
   constructor <;> intro h
   · cases' (eq_iff_exists M S).mp h with c hc
-    rw [mul_zero, mul_comm] at hc
+    rw [MulZeroClass.mul_zero, mul_comm] at hc
     exact hM c.2 x hc
   · rw [h]
 #align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iff
@@ -1946,7 +1946,7 @@ theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [Is
       have :
         z * w * algebraMap A S y.2 * algebraMap A S x.2 = algebraMap A S x.1 * algebraMap A S y.1 :=
         by rw [mul_assoc z, hy, ← hx] <;> ring
-      rw [h, zero_mul, zero_mul, ← (algebraMap A S).map_mul] at this
+      rw [h, MulZeroClass.zero_mul, MulZeroClass.zero_mul, ← (algebraMap A S).map_mul] at this
       cases' eq_zero_or_eq_zero_of_mul_eq_zero ((to_map_eq_zero_iff S hM).mp this.symm) with H H
       · exact Or.inl (eq_zero_of_fst_eq_zero hx H)
       · exact Or.inr (eq_zero_of_fst_eq_zero hy H) }

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -97,6 +97,7 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 
 variable [Algebra R S] {P : Type _} [CommSemiring P]
 
+#print IsLocalization /-
 /- ./././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] [] -/
@@ -107,6 +108,7 @@ class IsLocalization : Prop where
   surj : ∀ z : S, ∃ x : R × M, z * algebraMap R S x.2 = algebraMap R S x.1
   eq_iff_exists : ∀ {x y}, algebraMap R S x = algebraMap R S y ↔ ∃ c : M, ↑c * x = ↑c * y
 #align is_localization IsLocalization
+-/
 
 variable {M S}
 
@@ -120,6 +122,12 @@ section
 
 variable (M)
 
+/- warning: is_localization.of_le -> IsLocalization.of_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M N) -> (forall (r : 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.hasMem.{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)))))) r N) -> (IsUnit.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) r))) -> (IsLocalization.{u1, u2} R _inst_1 N S _inst_2 _inst_3)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (N : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))), (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} 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(CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) r))) -> (IsLocalization.{u2, u1} R _inst_1 N S _inst_2 _inst_3)
+Case conversion may be inaccurate. Consider using '#align is_localization.of_le IsLocalization.of_leₓ'. -/
 theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (algebraMap R S r)) :
     IsLocalization N S :=
   { map_units := fun r => h₂ r r.2
@@ -138,6 +146,7 @@ theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (al
 
 variable (S)
 
+#print IsLocalization.toLocalizationWithZeroMap /-
 /-- `is_localization.to_localization_with_zero_map M S` shows `S` is the monoid localization of
 `R` at `M`. -/
 @[simps]
@@ -148,17 +157,32 @@ def toLocalizationWithZeroMap : Submonoid.LocalizationWithZeroMap M S :=
     surj' := IsLocalization.surj _
     eq_iff_exists' := fun _ _ => IsLocalization.eq_iff_exists _ _ }
 #align is_localization.to_localization_with_zero_map IsLocalization.toLocalizationWithZeroMap
+-/
 
+#print IsLocalization.toLocalizationMap /-
 /-- `is_localization.to_localization_map M S` shows `S` is the monoid localization of `R` at `M`. -/
 abbrev toLocalizationMap : Submonoid.LocalizationMap M S :=
   (toLocalizationWithZeroMap M S).toLocalizationMap
 #align is_localization.to_localization_map IsLocalization.toLocalizationMap
+-/
 
+/- warning: is_localization.to_localization_map_to_map -> IsLocalization.toLocalizationMap_toMap is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_localization.to_localization_map_to_map IsLocalization.toLocalizationMap_toMapₓ'. -/
 @[simp]
 theorem toLocalizationMap_toMap : (toLocalizationMap M S).toMap = (algebraMap R S : R →*₀ S) :=
   rfl
 #align is_localization.to_localization_map_to_map IsLocalization.toLocalizationMap_toMap
 
+/- warning: is_localization.to_localization_map_to_map_apply -> IsLocalization.toLocalizationMap_toMap_apply is a dubious translation:
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 theorem toLocalizationMap_toMap_apply (x) : (toLocalizationMap M S).toMap x = algebraMap R S x :=
   rfl
 #align is_localization.to_localization_map_to_map_apply IsLocalization.toLocalizationMap_toMap_apply
@@ -167,17 +191,35 @@ end
 
 variable (M)
 
+/- warning: is_localization.sec -> IsLocalization.sec is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.sec IsLocalization.secₓ'. -/
 /-- Given a localization map `f : M →* N`, a section function sending `z : N` to some
 `(x, y) : M × S` such that `f x * (f y)⁻¹ = z`. -/
 noncomputable def sec (z : S) : R × M :=
   Classical.choose <| IsLocalization.surj _ z
 #align is_localization.sec IsLocalization.sec
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.to_localization_map_sec IsLocalization.toLocalizationMap_secₓ'. -/
 @[simp]
 theorem toLocalizationMap_sec : (toLocalizationMap M S).sec = sec M :=
   rfl
 #align is_localization.to_localization_map_sec IsLocalization.toLocalizationMap_sec
 
+/- warning: is_localization.sec_spec -> IsLocalization.sec_spec is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.sec_spec IsLocalization.sec_specₓ'. -/
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x` (so this lemma is true by definition). -/
 theorem sec_spec (z : S) :
@@ -185,6 +227,12 @@ theorem sec_spec (z : S) :
   Classical.choose_spec <| IsLocalization.surj _ z
 #align is_localization.sec_spec IsLocalization.sec_spec
 
+/- warning: is_localization.sec_spec' -> IsLocalization.sec_spec' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.sec_spec' IsLocalization.sec_spec'ₓ'. -/
 /-- Given `z : S`, `is_localization.sec M z` is defined to be a pair `(x, y) : R × M` such
 that `z * f y = f x`, so this lemma is just an application of `S`'s commutativity. -/
 theorem sec_spec' (z : S) :
@@ -194,16 +242,34 @@ theorem sec_spec' (z : S) :
 
 variable {R M}
 
+/- warning: is_localization.map_right_cancel -> IsLocalization.map_right_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_localization.map_right_cancel IsLocalization.map_right_cancelₓ'. -/
 theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap R S (c * y)) :
     algebraMap R S x = algebraMap R S y :=
   (toLocalizationMap M S).map_right_cancel h
 #align is_localization.map_right_cancel IsLocalization.map_right_cancel
 
+/- warning: is_localization.map_left_cancel -> IsLocalization.map_left_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_localization.map_left_cancel IsLocalization.map_left_cancelₓ'. -/
 theorem map_left_cancel {x y} {c : M} (h : algebraMap R S (x * c) = algebraMap R S (y * c)) :
     algebraMap R S x = algebraMap R S y :=
   (toLocalizationMap M S).map_left_cancel h
 #align is_localization.map_left_cancel IsLocalization.map_left_cancel
 
+/- warning: is_localization.eq_zero_of_fst_eq_zero -> IsLocalization.eq_zero_of_fst_eq_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_localization.eq_zero_of_fst_eq_zero IsLocalization.eq_zero_of_fst_eq_zeroₓ'. -/
 theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebraMap R S x)
     (hx : x = 0) : z = 0 := by
   rw [hx, (algebraMap R S).map_zero] at h
@@ -212,6 +278,12 @@ theorem eq_zero_of_fst_eq_zero {z x} {y : M} (h : z * algebraMap R S y = algebra
 
 variable (M S)
 
+/- warning: is_localization.map_eq_zero_iff -> IsLocalization.map_eq_zero_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_localization.map_eq_zero_iff IsLocalization.map_eq_zero_iffₓ'. -/
 theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r = 0 :=
   by
   constructor
@@ -225,41 +297,85 @@ theorem map_eq_zero_iff (r : R) : algebraMap R S r = 0 ↔ ∃ m : M, ↑m * r =
 
 variable {M}
 
+/- warning: is_localization.mk' -> IsLocalization.mk' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk' IsLocalization.mk'ₓ'. -/
 /-- `is_localization.mk' S` is the surjection sending `(x, y) : R × M` to
 `f x * (f y)⁻¹`. -/
 noncomputable def mk' (x : R) (y : M) : S :=
   (toLocalizationMap M S).mk' x y
 #align is_localization.mk' IsLocalization.mk'
 
+#print IsLocalization.mk'_sec /-
 @[simp]
 theorem mk'_sec (z : S) : mk' S (IsLocalization.sec M z).1 (IsLocalization.sec M z).2 = z :=
   (toLocalizationMap M S).mk'_sec _
 #align is_localization.mk'_sec IsLocalization.mk'_sec
+-/
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul IsLocalization.mk'_mulₓ'. -/
 theorem mk'_mul (x₁ x₂ : R) (y₁ y₂ : M) : mk' S (x₁ * x₂) (y₁ * y₂) = mk' S x₁ y₁ * mk' S x₂ y₂ :=
   (toLocalizationMap M S).mk'_mul _ _ _ _
 #align is_localization.mk'_mul IsLocalization.mk'_mul
 
+/- warning: is_localization.mk'_one -> IsLocalization.mk'_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_one IsLocalization.mk'_oneₓ'. -/
 theorem mk'_one (x) : mk' S x (1 : M) = algebraMap R S x :=
   (toLocalizationMap M S).mk'_one _
 #align is_localization.mk'_one IsLocalization.mk'_one
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec IsLocalization.mk'_specₓ'. -/
 @[simp]
 theorem mk'_spec (x) (y : M) : mk' S x y * algebraMap R S y = algebraMap R S x :=
   (toLocalizationMap M S).mk'_spec _ _
 #align is_localization.mk'_spec IsLocalization.mk'_spec
 
+/- warning: is_localization.mk'_spec' -> IsLocalization.mk'_spec' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec' IsLocalization.mk'_spec'ₓ'. -/
 @[simp]
 theorem mk'_spec' (x) (y : M) : algebraMap R S y * mk' S x y = algebraMap R S x :=
   (toLocalizationMap M S).mk'_spec' _ _
 #align is_localization.mk'_spec' IsLocalization.mk'_spec'
 
+/- warning: is_localization.mk'_spec_mk -> IsLocalization.mk'_spec_mk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_spec_mk IsLocalization.mk'_spec_mkₓ'. -/
 @[simp]
 theorem mk'_spec_mk (x) (y : R) (hy : y ∈ M) :
     mk' S x ⟨y, hy⟩ * algebraMap R S y = algebraMap R S x :=
   mk'_spec S x ⟨y, hy⟩
 #align is_localization.mk'_spec_mk IsLocalization.mk'_spec_mk
 
+/- warning: is_localization.mk'_spec'_mk -> IsLocalization.mk'_spec'_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_localization.mk'_spec'_mk IsLocalization.mk'_spec'_mkₓ'. -/
 @[simp]
 theorem mk'_spec'_mk (x) (y : R) (hy : y ∈ M) :
     algebraMap R S y * mk' S x ⟨y, hy⟩ = algebraMap R S x :=
@@ -268,16 +384,34 @@ theorem mk'_spec'_mk (x) (y : R) (hy : y ∈ M) :
 
 variable {S}
 
+/- warning: is_localization.eq_mk'_iff_mul_eq -> IsLocalization.eq_mk'_iff_mul_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.eq_mk'_iff_mul_eq IsLocalization.eq_mk'_iff_mul_eqₓ'. -/
 theorem eq_mk'_iff_mul_eq {x} {y : M} {z} :
     z = mk' S x y ↔ z * algebraMap R S y = algebraMap R S x :=
   (toLocalizationMap M S).eq_mk'_iff_mul_eq
 #align is_localization.eq_mk'_iff_mul_eq IsLocalization.eq_mk'_iff_mul_eq
 
+/- warning: is_localization.mk'_eq_iff_eq_mul -> IsLocalization.mk'_eq_iff_eq_mul 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_localization.mk'_eq_iff_eq_mul IsLocalization.mk'_eq_iff_eq_mulₓ'. -/
 theorem mk'_eq_iff_eq_mul {x} {y : M} {z} :
     mk' S x y = z ↔ algebraMap R S x = z * algebraMap R S y :=
   (toLocalizationMap M S).mk'_eq_iff_eq_mul
 #align is_localization.mk'_eq_iff_eq_mul IsLocalization.mk'_eq_iff_eq_mul
 
+/- warning: is_localization.mk'_add_eq_iff_add_mul_eq_mul -> IsLocalization.mk'_add_eq_iff_add_mul_eq_mul is a dubious translation:
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+but is expected to have type
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(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))))) M)) y))))
+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_add_eq_iff_add_mul_eq_mul IsLocalization.mk'_add_eq_iff_add_mul_eq_mulₓ'. -/
 theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
     mk' S x y + z₁ = z₂ ↔ algebraMap R S x + z₁ * algebraMap R S y = z₂ * algebraMap R S y := by
   rw [← mk'_spec S x y, ← IsUnit.mul_left_inj (IsLocalization.map_units S y), right_distrib]
@@ -285,6 +419,12 @@ theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
 
 variable (M)
 
+/- warning: is_localization.mk'_surjective -> IsLocalization.mk'_surjective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_surjective IsLocalization.mk'_surjectiveₓ'. -/
 theorem mk'_surjective (z : S) : ∃ (x : _)(y : M), mk' S x y = z :=
   let ⟨r, hr⟩ := IsLocalization.surj _ z
   ⟨r.1, r.2, (eq_mk'_iff_mul_eq.2 hr).symm⟩
@@ -294,32 +434,58 @@ variable (S)
 
 include M
 
+#print IsLocalization.fintype' /-
 /-- The localization of a `fintype` is a `fintype`. Cannot be an instance. -/
 noncomputable def fintype' [Fintype R] : Fintype S :=
   have := Classical.propDecidable
   Fintype.ofSurjective (Function.uncurry <| IsLocalization.mk' S) fun a =>
     prod.exists'.mpr <| IsLocalization.mk'_surjective M a
 #align is_localization.fintype' IsLocalization.fintype'
+-/
 
 omit M
 
 variable {M S}
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.unique_of_zero_mem IsLocalization.uniqueOfZeroMemₓ'. -/
 /-- Localizing at a submonoid with 0 inside it leads to the trivial ring. -/
 def uniqueOfZeroMem (h : (0 : R) ∈ M) : Unique S :=
   uniqueOfZeroEqOne <| by simpa using IsLocalization.map_units S ⟨0, h⟩
 #align is_localization.unique_of_zero_mem IsLocalization.uniqueOfZeroMem
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_eq IsLocalization.mk'_eq_iff_eqₓ'. -/
 theorem mk'_eq_iff_eq {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (y₂ * x₁) = algebraMap R S (y₁ * x₂) :=
   (toLocalizationMap M S).mk'_eq_iff_eq
 #align is_localization.mk'_eq_iff_eq IsLocalization.mk'_eq_iff_eq
 
+/- warning: is_localization.mk'_eq_iff_eq' -> IsLocalization.mk'_eq_iff_eq' 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_localization.mk'_eq_iff_eq' IsLocalization.mk'_eq_iff_eq'ₓ'. -/
 theorem mk'_eq_iff_eq' {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ algebraMap R S (x₁ * y₂) = algebraMap R S (x₂ * y₁) :=
   (toLocalizationMap M S).mk'_eq_iff_eq'
 #align is_localization.mk'_eq_iff_eq' IsLocalization.mk'_eq_iff_eq'
 
+/- warning: is_localization.mk'_mem_iff -> IsLocalization.mk'_mem_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iffₓ'. -/
 theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R S x ∈ I :=
   by
   constructor <;> intro h
@@ -331,20 +497,44 @@ theorem mk'_mem_iff {x} {y : M} {I : Ideal S} : mk' S x y ∈ I ↔ algebraMap R
     rwa [mul_comm, mul_assoc, hb, mul_one] at this
 #align is_localization.mk'_mem_iff IsLocalization.mk'_mem_iff
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localization.eq IsLocalization.eqₓ'. -/
 protected theorem eq {a₁ b₁} {a₂ b₂ : M} :
     mk' S a₁ a₂ = mk' S b₁ b₂ ↔ ∃ c : M, ↑c * (↑b₂ * a₁) = c * (a₂ * b₁) :=
   (toLocalizationMap M S).Eq
 #align is_localization.eq IsLocalization.eq
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_zero_iff IsLocalization.mk'_eq_zero_iffₓ'. -/
 theorem mk'_eq_zero_iff (x : R) (s : M) : mk' S x s = 0 ↔ ∃ m : M, ↑m * x = 0 := by
   rw [← (map_units S s).mul_left_inj, mk'_spec, zero_mul, map_eq_zero_iff M]
 #align is_localization.mk'_eq_zero_iff IsLocalization.mk'_eq_zero_iff
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_zero IsLocalization.mk'_zeroₓ'. -/
 @[simp]
 theorem mk'_zero (s : M) : IsLocalization.mk' S 0 s = 0 := by
   rw [eq_comm, IsLocalization.eq_mk'_iff_mul_eq, zero_mul, map_zero]
 #align is_localization.mk'_zero IsLocalization.mk'_zero
 
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+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {x : R} {y : 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 M)}, (Ne.{succ u1} S (IsLocalization.mk'.{u2, u1} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y) (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))))) -> (Ne.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align is_localization.ne_zero_of_mk'_ne_zero IsLocalization.ne_zero_of_mk'_ne_zeroₓ'. -/
 theorem ne_zero_of_mk'_ne_zero {x : R} {y : M} (hxy : IsLocalization.mk' S x y ≠ 0) : x ≠ 0 :=
   by
   rintro rfl
@@ -355,21 +545,45 @@ section Ext
 
 variable [Algebra R P] [IsLocalization M P]
 
+/- warning: is_localization.eq_iff_eq -> IsLocalization.eq_iff_eq 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_localization.eq_iff_eq IsLocalization.eq_iff_eqₓ'. -/
 theorem eq_iff_eq {x y} :
     algebraMap R S x = algebraMap R S y ↔ algebraMap R P x = algebraMap R P y :=
   (toLocalizationMap M S).eq_iff_eq (toLocalizationMap M P)
 #align is_localization.eq_iff_eq IsLocalization.eq_iff_eq
 
+/- warning: is_localization.mk'_eq_iff_mk'_eq -> IsLocalization.mk'_eq_iff_mk'_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_iff_mk'_eq IsLocalization.mk'_eq_iff_mk'_eqₓ'. -/
 theorem mk'_eq_iff_mk'_eq {x₁ x₂} {y₁ y₂ : M} :
     mk' S x₁ y₁ = mk' S x₂ y₂ ↔ mk' P x₁ y₁ = mk' P x₂ y₂ :=
   (toLocalizationMap M S).mk'_eq_iff_mk'_eq (toLocalizationMap M P)
 #align is_localization.mk'_eq_iff_mk'_eq IsLocalization.mk'_eq_iff_mk'_eq
 
+/- warning: is_localization.mk'_eq_of_eq -> IsLocalization.mk'_eq_of_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_of_eq IsLocalization.mk'_eq_of_eqₓ'. -/
 theorem mk'_eq_of_eq {a₁ b₁ : R} {a₂ b₂ : M} (H : ↑a₂ * b₁ = ↑b₂ * a₁) :
     mk' S a₁ a₂ = mk' S b₁ b₂ :=
   (toLocalizationMap M S).mk'_eq_of_eq H
 #align is_localization.mk'_eq_of_eq IsLocalization.mk'_eq_of_eq
 
+/- warning: is_localization.mk'_eq_of_eq' -> IsLocalization.mk'_eq_of_eq' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_of_eq' IsLocalization.mk'_eq_of_eq'ₓ'. -/
 theorem mk'_eq_of_eq' {a₁ b₁ : R} {a₂ b₂ : M} (H : b₁ * ↑a₂ = a₁ * ↑b₂) :
     mk' S a₁ a₂ = mk' S b₁ b₂ :=
   (toLocalizationMap M S).mk'_eq_of_eq' H
@@ -377,45 +591,99 @@ theorem mk'_eq_of_eq' {a₁ b₁ : R} {a₂ b₂ : M} (H : b₁ * ↑a₂ = a₁
 
 variable (S)
 
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 @[simp]
 theorem mk'_self {x : R} (hx : x ∈ M) : mk' S x ⟨x, hx⟩ = 1 :=
   (toLocalizationMap M S).mk'_self _ hx
 #align is_localization.mk'_self IsLocalization.mk'_self
 
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 @[simp]
 theorem mk'_self' {x : M} : mk' S (x : R) x = 1 :=
   (toLocalizationMap M S).mk'_self' _
 #align is_localization.mk'_self' IsLocalization.mk'_self'
 
+/- warning: is_localization.mk'_self'' -> IsLocalization.mk'_self'' is a dubious translation:
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 theorem mk'_self'' {x : M} : mk' S x.1 x = 1 :=
   mk'_self' _
 #align is_localization.mk'_self'' IsLocalization.mk'_self''
 
 end Ext
 
+/- warning: is_localization.mul_mk'_eq_mk'_of_mul -> IsLocalization.mul_mk'_eq_mk'_of_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mul_mk'_eq_mk'_of_mul IsLocalization.mul_mk'_eq_mk'_of_mulₓ'. -/
 theorem mul_mk'_eq_mk'_of_mul (x y : R) (z : M) :
     (algebraMap R S) x * mk' S y z = mk' S (x * y) z :=
   (toLocalizationMap M S).mul_mk'_eq_mk'_of_mul _ _ _
 #align is_localization.mul_mk'_eq_mk'_of_mul IsLocalization.mul_mk'_eq_mk'_of_mul
 
+/- warning: is_localization.mk'_eq_mul_mk'_one -> IsLocalization.mk'_eq_mul_mk'_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_eq_mul_mk'_one IsLocalization.mk'_eq_mul_mk'_oneₓ'. -/
 theorem mk'_eq_mul_mk'_one (x : R) (y : M) : mk' S x y = (algebraMap R S) x * mk' S 1 y :=
   ((toLocalizationMap M S).mul_mk'_one_eq_mk' _ _).symm
 #align is_localization.mk'_eq_mul_mk'_one IsLocalization.mk'_eq_mul_mk'_one
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_cancel_left IsLocalization.mk'_mul_cancel_leftₓ'. -/
 @[simp]
 theorem mk'_mul_cancel_left (x : R) (y : M) : mk' S (y * x : R) y = (algebraMap R S) x :=
   (toLocalizationMap M S).mk'_mul_cancel_left _ _
 #align is_localization.mk'_mul_cancel_left IsLocalization.mk'_mul_cancel_left
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_cancel_right IsLocalization.mk'_mul_cancel_rightₓ'. -/
 theorem mk'_mul_cancel_right (x : R) (y : M) : mk' S (x * y) y = (algebraMap R S) x :=
   (toLocalizationMap M S).mk'_mul_cancel_right _ _
 #align is_localization.mk'_mul_cancel_right IsLocalization.mk'_mul_cancel_right
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_mk'_eq_one IsLocalization.mk'_mul_mk'_eq_oneₓ'. -/
 @[simp]
 theorem mk'_mul_mk'_eq_one (x y : M) : mk' S (x : R) y * mk' S (y : R) x = 1 := by
   rw [← mk'_mul, mul_comm] <;> exact mk'_self _ _
 #align is_localization.mk'_mul_mk'_eq_one IsLocalization.mk'_mul_mk'_eq_one
 
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_mul_mk'_eq_one' IsLocalization.mk'_mul_mk'_eq_one'ₓ'. -/
 theorem mk'_mul_mk'_eq_one' (x : R) (y : M) (h : x ∈ M) : mk' S x y * mk' S (y : R) ⟨x, h⟩ = 1 :=
   mk'_mul_mk'_eq_one ⟨x, h⟩ _
 #align is_localization.mk'_mul_mk'_eq_one' IsLocalization.mk'_mul_mk'_eq_one'
@@ -424,12 +692,24 @@ section
 
 variable (M)
 
+/- warning: is_localization.is_unit_comp -> IsLocalization.isUnit_comp 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_localization.is_unit_comp IsLocalization.isUnit_compₓ'. -/
 theorem isUnit_comp (j : S →+* P) (y : M) : IsUnit (j.comp (algebraMap R S) y) :=
   (toLocalizationMap M S).isUnit_comp j.toMonoidHom _
 #align is_localization.is_unit_comp IsLocalization.isUnit_comp
 
 end
 
+/- warning: is_localization.eq_of_eq -> IsLocalization.eq_of_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 is_localization.eq_of_eq IsLocalization.eq_of_eqₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g(M) ⊆ units P`, `f x = f y → g x = g y` for all `x y : R`. -/
 theorem eq_of_eq {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) {x y}
@@ -437,6 +717,12 @@ theorem eq_of_eq {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) {x y}
   @Submonoid.LocalizationMap.eq_of_eq _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom hg _ _ h
 #align is_localization.eq_of_eq IsLocalization.eq_of_eq
 
+/- warning: is_localization.mk'_add -> IsLocalization.mk'_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.mk'_add IsLocalization.mk'_addₓ'. -/
 theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
     mk' S (x₁ * y₂ + x₂ * y₁) (y₁ * y₂) = mk' S x₁ y₁ + mk' S x₂ y₂ :=
   mk'_eq_iff_eq_mul.2 <|
@@ -449,6 +735,12 @@ theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
         ring)
 #align is_localization.mk'_add IsLocalization.mk'_add
 
+/- warning: is_localization.mul_add_inv_left -> IsLocalization.mul_add_inv_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_localization.mul_add_inv_left IsLocalization.mul_add_inv_leftₓ'. -/
 theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (w z₁ z₂ : P) :
     w * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) h y)⁻¹ + z₁ = z₂ ↔ w + g y * z₁ = g y * z₂ :=
   by
@@ -458,6 +750,12 @@ theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (
   simp only [RingHom.toMonoidHom_eq_coe, MonoidHom.restrict_apply, [anonymous]]
 #align is_localization.mul_add_inv_left IsLocalization.mul_add_inv_left
 
+/- warning: is_localization.lift_spec_mul_add -> IsLocalization.lift_spec_mul_add is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) x M)), IsUnit.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (MonoidWithZero.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g (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 _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) M)) y))) (z : S) (w : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (w' : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (v : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (HAdd.hAdd.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (instHAdd.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (Distrib.toAdd.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (NonUnitalNonAssocSemiring.toDistrib.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) _inst_4)))))) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) z) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S P (MulOneClass.toMul.{u1} S (MulZeroOneClass.toMulOneClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))))) (MulOneClass.toMul.{u2} P (MulZeroOneClass.toMulOneClass.{u2} P (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidWithZeroHom.{u1, u2} S P (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u2} P (CommMonoidWithZero.toMonoidWithZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P _inst_4)))) S P (MulZeroOneClass.toMulOneClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (CommMonoidWithZero.toMonoidWithZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S _inst_2)))) (MulZeroOneClass.toMulOneClass.{u2} P 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+Case conversion may be inaccurate. Consider using '#align is_localization.lift_spec_mul_add IsLocalization.lift_spec_mul_addₓ'. -/
 theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w' v) :
     ((toLocalizationWithZeroMap M S).lift g.toMonoidWithZeroHom hg) z * w + w' = v ↔
       g ((toLocalizationMap M S).sec z).1 * w + g ((toLocalizationMap M S).sec z).2 * w' =
@@ -468,6 +766,12 @@ theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w'
   rfl
 #align is_localization.lift_spec_mul_add IsLocalization.lift_spec_mul_add
 
+/- warning: is_localization.lift -> IsLocalization.lift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.lift IsLocalization.liftₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →+* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
 `S` to `P` sending `z : S` to `g x * (g y)⁻¹`, where `(x, y) : R × M` are such that
@@ -490,6 +794,12 @@ noncomputable def lift {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) : S →+*
 
 variable {g : R →+* P} (hg : ∀ y : M, IsUnit (g y))
 
+/- warning: is_localization.lift_mk' -> IsLocalization.lift_mk' is a dubious translation:
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M) hg) y))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk' IsLocalization.lift_mk'ₓ'. -/
 /-- Given a localization map `f : R →+* S` for a submonoid `M ⊆ R` and a map of `comm_semiring`s
 `g : R →* P` such that `g y` is invertible for all `y : M`, the homomorphism induced from
 `S` to `P` maps `f x * (f y)⁻¹` to `g x * (g y)⁻¹` for all `x : R, y ∈ M`. -/
@@ -498,25 +808,55 @@ theorem lift_mk' (x y) :
   (toLocalizationMap M S).lift_mk' _ _ _
 #align is_localization.lift_mk' IsLocalization.lift_mk'
 
+/- warning: is_localization.lift_mk'_spec -> IsLocalization.lift_mk'_spec is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _inst_1))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R 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+Case conversion may be inaccurate. Consider using '#align is_localization.lift_mk'_spec IsLocalization.lift_mk'_specₓ'. -/
 theorem lift_mk'_spec (x v) (y : M) : lift hg (mk' S x y) = v ↔ g x = g y * v :=
   (toLocalizationMap M S).lift_mk'_spec _ _ _ _
 #align is_localization.lift_mk'_spec IsLocalization.lift_mk'_spec
 
+/- warning: is_localization.lift_eq -> IsLocalization.lift_eq is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} (hg : forall (y : 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 M)), IsUnit.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (MonoidWithZero.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{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))))) M)) y)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u3} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) g (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, 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+Case conversion may be inaccurate. Consider using '#align is_localization.lift_eq IsLocalization.lift_eqₓ'. -/
 @[simp]
 theorem lift_eq (x : R) : lift hg ((algebraMap R S) x) = g x :=
   (toLocalizationMap M S).liftEq _ _
 #align is_localization.lift_eq IsLocalization.lift_eq
 
+/- warning: is_localization.lift_eq_iff -> IsLocalization.lift_eq_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 _inst_1))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R 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+Case conversion may be inaccurate. Consider using '#align is_localization.lift_eq_iff IsLocalization.lift_eq_iffₓ'. -/
 theorem lift_eq_iff {x y : R × M} :
     lift hg (mk' S x.1 x.2) = lift hg (mk' S y.1 y.2) ↔ g (x.1 * y.2) = g (y.1 * x.2) :=
   (toLocalizationMap M S).lift_eq_iff _
 #align is_localization.lift_eq_iff IsLocalization.lift_eq_iff
 
+/- warning: is_localization.lift_comp -> IsLocalization.lift_comp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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 @[simp]
 theorem lift_comp : (lift hg).comp (algebraMap R S) = g :=
   RingHom.ext <| MonoidHom.ext_iff.1 <| (toLocalizationMap M S).lift_comp _
 #align is_localization.lift_comp IsLocalization.lift_comp
 
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 @[simp]
 theorem lift_of_comp (j : S →+* P) : lift (isUnit_comp M j) = j :=
   RingHom.ext <| MonoidHom.ext_iff.1 <| (toLocalizationMap M S).lift_of_comp j.toMonoidHom
@@ -524,18 +864,36 @@ theorem lift_of_comp (j : S →+* P) : lift (isUnit_comp M j) = j :=
 
 variable (M)
 
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(NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) j (MonoidHomClass.toMonoidHom.{u1, u3, max u1 u3} R S (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} S (NonAssocSemiring.toMulZeroOneClass.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3))) (MonoidHom.comp.{u1, u3, u2} R S P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} S (NonAssocSemiring.toMulZeroOneClass.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) k (MonoidHomClass.toMonoidHom.{u1, u3, max u1 u3} R S (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} S (NonAssocSemiring.toMulZeroOneClass.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3)))) -> (Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} S P (MulZeroOneClass.toMulOneClass.{u3} S (NonAssocSemiring.toMulZeroOneClass.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) j k)
+Case conversion may be inaccurate. Consider using '#align is_localization.monoid_hom_ext IsLocalization.monoidHom_extₓ'. -/
 /-- See note [partially-applied ext lemmas] -/
 theorem monoidHom_ext ⦃j k : S →* P⦄
     (h : j.comp (algebraMap R S : R →* S) = k.comp (algebraMap R S)) : j = k :=
   Submonoid.LocalizationMap.epic_of_localizationMap (toLocalizationMap M S) <| MonoidHom.congr_fun h
 #align is_localization.monoid_hom_ext IsLocalization.monoidHom_ext
 
+/- warning: is_localization.ring_hom_ext -> IsLocalization.ringHom_ext is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {{j : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}} {{k : RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))}}, (Eq.{max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHom.comp.{u1, u2, u3} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) (RingHom.comp.{u1, u2, u3} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) k (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3))) -> (Eq.{max (succ u2) (succ u3)} (RingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) j k)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {{j : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))}} {{k : RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))}}, (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHom.comp.{u1, u3, u2} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) j (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3)) (RingHom.comp.{u1, u3, u2} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) k (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3))) -> (Eq.{max (succ u3) (succ u2)} (RingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) j k)
+Case conversion may be inaccurate. Consider using '#align is_localization.ring_hom_ext IsLocalization.ringHom_extₓ'. -/
 /-- See note [partially-applied ext lemmas] -/
 theorem ringHom_ext ⦃j k : S →+* P⦄ (h : j.comp (algebraMap R S) = k.comp (algebraMap R S)) :
     j = k :=
   RingHom.coe_monoidHom_injective <| monoidHom_ext M <| MonoidHom.ext <| RingHom.congr_fun h
 #align is_localization.ring_hom_ext IsLocalization.ringHom_ext
 
+/- warning: is_localization.alg_hom_subsingleton -> IsLocalization.algHom_subsingleton is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R P _inst_1 (CommSemiring.toSemiring.{u3} P _inst_4)], Subsingleton.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R S P _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u3} P _inst_4) _inst_3 _inst_6)
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u2} R P _inst_1 (CommSemiring.toSemiring.{u2} P _inst_4)], Subsingleton.{max (succ u2) (succ u1)} (AlgHom.{u3, u1, u2} R S P _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} P _inst_4) _inst_3 _inst_6)
+Case conversion may be inaccurate. Consider using '#align is_localization.alg_hom_subsingleton IsLocalization.algHom_subsingletonₓ'. -/
 /- This is not an instance because the submonoid `M` would become a metavariable
   in typeclass search. -/
 theorem algHom_subsingleton [Algebra R P] : Subsingleton (S →ₐ[R] P) :=
@@ -544,6 +902,12 @@ theorem algHom_subsingleton [Algebra R P] : Subsingleton (S →ₐ[R] P) :=
       IsLocalization.ringHom_ext M <| by rw [f.comp_algebra_map, g.comp_algebra_map]⟩
 #align is_localization.alg_hom_subsingleton IsLocalization.algHom_subsingleton
 
+/- warning: is_localization.ext -> IsLocalization.ext is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : S -> P) (k : S -> P), (Eq.{succ u3} P (j (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (OfNat.ofNat.{u3} P 1 (OfNat.mk.{u3} P 1 (One.one.{u3} P (AddMonoidWithOne.toOne.{u3} P (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} P (NonAssocSemiring.toAddCommMonoidWithOne.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) -> (Eq.{succ u3} P (k (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))))) (OfNat.ofNat.{u3} P 1 (OfNat.mk.{u3} P 1 (One.one.{u3} P (AddMonoidWithOne.toOne.{u3} P (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} P (NonAssocSemiring.toAddCommMonoidWithOne.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) -> (forall (a : S) (b : S), Eq.{succ u3} P (j (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) (j a) (j b))) -> (forall (a : S) (b : S), Eq.{succ u3} P (k (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) a b)) (HMul.hMul.{u3, u3, u3} P P P (instHMul.{u3} P (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) (k a) (k b))) -> (forall (a : R), Eq.{succ u3} P (j (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a)) (k (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) a))) -> (Eq.{max (succ u2) (succ u3)} (S -> P) j k)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (j : S -> P) (k : S -> P), (Eq.{succ u3} P (j (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> (Eq.{succ u3} P (k (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (OfNat.ofNat.{u3} P 1 (One.toOfNat1.{u3} P (Semiring.toOne.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) -> 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+Case conversion may be inaccurate. Consider using '#align is_localization.ext IsLocalization.extₓ'. -/
 /-- To show `j` and `k` agree on the whole localization, it suffices to show they agree
 on the image of the base ring, if they preserve `1` and `*`. -/
 protected theorem ext (j k : S → P) (hj1 : j 1 = 1) (hk1 : k 1 = 1)
@@ -554,6 +918,12 @@ protected theorem ext (j k : S → P) (hj1 : j 1 = 1) (hk1 : k 1 = 1)
 
 variable {M}
 
+/- warning: is_localization.lift_unique -> IsLocalization.lift_unique is a dubious translation:
+lean 3 declaration is
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_inst_4 _inst_5 g hg) j)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 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(Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (IsLocalization.lift.{u1, u3, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 g hg) j)
+Case conversion may be inaccurate. Consider using '#align is_localization.lift_unique IsLocalization.lift_uniqueₓ'. -/
 theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) : lift hg = j :=
   RingHom.ext <|
     MonoidHom.ext_iff.1 <|
@@ -561,16 +931,34 @@ theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) :
         j.toMonoidHom hj
 #align is_localization.lift_unique IsLocalization.lift_unique
 
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 @[simp]
 theorem lift_id (x) : lift (map_units S : ∀ y : M, IsUnit _) x = x :=
   (toLocalizationMap M S).lift_id _
 #align is_localization.lift_id IsLocalization.lift_id
 
+/- warning: is_localization.lift_surjective_iff -> IsLocalization.lift_surjective_iff is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 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+Case conversion may be inaccurate. Consider using '#align is_localization.lift_surjective_iff IsLocalization.lift_surjective_iffₓ'. -/
 theorem lift_surjective_iff :
     Surjective (lift hg : S → P) ↔ ∀ v : P, ∃ x : R × M, v * g x.2 = g x.1 :=
   (toLocalizationMap M S).lift_surjective_iff hg
 #align is_localization.lift_surjective_iff IsLocalization.lift_surjective_iff
 
+/- warning: is_localization.lift_injective_iff -> IsLocalization.lift_injective_iff is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))} (hg : forall (y : 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 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u3} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3) y)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P 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P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))) g y)))
+Case conversion may be inaccurate. Consider using '#align is_localization.lift_injective_iff IsLocalization.lift_injective_iffₓ'. -/
 theorem lift_injective_iff :
     Injective (lift hg : S → P) ↔ ∀ x y, algebraMap R S x = algebraMap R S y ↔ g x = g y :=
   (toLocalizationMap M S).lift_injective_iff hg
@@ -586,6 +974,12 @@ section
 
 variable (Q)
 
+/- warning: is_localization.map -> IsLocalization.map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} (Q : Type.{u4}) [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) -> (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} (Q : Type.{u4}) [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))), (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) -> (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))
+Case conversion may be inaccurate. Consider using '#align is_localization.map IsLocalization.mapₓ'. -/
 /-- Map a homomorphism `g : R →+* P` to `S →+* Q`, where `S` and `Q` are
 localizations of `R` and `P` at `M` and `T` respectively,
 such that `g(M) ⊆ T`.
@@ -598,31 +992,67 @@ noncomputable def map (g : R →+* P) (hy : M ≤ T.comap g) : S →+* Q :=
 
 end
 
+/- warning: is_localization.map_eq -> IsLocalization.map_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q 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(coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => P -> Q) (RingHom.hasCoeToFun.{u3, u4} P Q (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (algebraMap.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6) _inst_7) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) => Q) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) a) (MulHomClass.toFunLike.{max u3 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(CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))
+Case conversion may be inaccurate. Consider using '#align is_localization.map_eq IsLocalization.map_eqₓ'. -/
 theorem map_eq (x) : map Q g hy ((algebraMap R S) x) = algebraMap P Q (g x) :=
   lift_eq (fun y => map_units _ ⟨g y, hy y.2⟩) x
 #align is_localization.map_eq IsLocalization.map_eq
 
+/- warning: is_localization.map_comp -> IsLocalization.map_comp is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_localization.map_comp IsLocalization.map_compₓ'. -/
 @[simp]
 theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g :=
   lift_comp fun y => map_units _ ⟨g y, hy y.2⟩
 #align is_localization.map_comp IsLocalization.map_comp
 
+/- warning: is_localization.map_mk' -> IsLocalization.map_mk' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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)))))) M), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (IsLocalization.mk'.{u3, u4} P _inst_4 T Q _inst_6 _inst_7 _inst_8 (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g x) (Subtype.mk.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (SetLike.hasMem.{u3, u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) P (Submonoid.setLike.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) x T) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) g ((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 (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)))))) M) R (HasLiftT.mk.{succ u1, succ u1} (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)))))) M) R (CoeTCₓ.coe.{succ u1, succ u1} (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)))))) M) R (coeBase.{succ u1, succ u1} (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)))))) M) R (coeSubtype.{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.hasMem.{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)))))) x M))))) y)) (hy (Subtype.val.{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.hasMem.{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)))))) x M) y) (Subtype.property.{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.hasMem.{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)))))) x M) y))))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u4, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u4, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Preorder.toLE.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))))) M (Submonoid.comap.{u4, u1, max u4 u1} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u1} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (x : R) (y : 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 _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 _inst_1))))) R 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+Case conversion may be inaccurate. Consider using '#align is_localization.map_mk' IsLocalization.map_mk'ₓ'. -/
 theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.2⟩ :=
   @Submonoid.LocalizationMap.map_mk' _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom _
     (fun y => hy y.2) _ _ (toLocalizationMap T Q) _ _
 #align is_localization.map_mk' IsLocalization.map_mk'
 
+/- warning: is_localization.map_id -> IsLocalization.map_id is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (z : S) (h : optParam.{0} (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R 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(NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomClass.toMonoidHomClass.{u2, u2, u2} (RingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M)) 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))) M)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S) z) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u1} S S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (IsLocalization.map.{u2, u1, u2, u1} R _inst_1 M S _inst_2 _inst_3 R _inst_1 _inst_5 M S _inst_2 _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) h) z) z
+Case conversion may be inaccurate. Consider using '#align is_localization.map_id IsLocalization.map_idₓ'. -/
 @[simp]
 theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
     map S (RingHom.id _) h z = z :=
   lift_id _
 #align is_localization.map_id IsLocalization.map_id
 
+/- warning: is_localization.map_unique -> IsLocalization.map_unique is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))), (forall (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (fun (_x : RingHom.{u2, u4} S Q 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+but is expected to have type
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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u3} P _inst_4 T Q _inst_6 _inst_7] (j : RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))), (forall (x : R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (RingHom.{u2, u4} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S 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(CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g x))) -> (Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} S Q (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) (IsLocalization.map.{u2, u4, u1, u3} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) j)
+Case conversion may be inaccurate. Consider using '#align is_localization.map_unique IsLocalization.map_uniqueₓ'. -/
 theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algebraMap P Q (g x)) :
     map Q g hy = j :=
   lift_unique (fun y => map_units _ ⟨g y, hy y.2⟩) hj
 #align is_localization.map_unique IsLocalization.map_unique
 
+/- warning: is_localization.map_comp_map -> IsLocalization.map_comp_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toLE.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)), Eq.{max (succ u2) (succ u6)} (RingHom.{u2, u6} S W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (RingHom.comp.{u2, u4, u6} S Q W (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10)) (IsLocalization.map.{u3, u4, u5, u6} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u2, u5, u6} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u3, u5} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) l g) (fun (x : R) (hx : 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.hasMem.{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)))))) x M) => hl (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (fun (_x : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) => R -> P) (FunLike.hasCoeToFun.{succ (max u1 u3), succ u1, succ u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R (fun (_x : R) => P) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulOneClass.toHasMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toHasMul.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) g x) (hy x hx)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u2}} [_inst_6 : CommSemiring.{u2} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u2} P Q _inst_4 (CommSemiring.toSemiring.{u2} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u2} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)), Eq.{max (succ u3) (succ u5)} (RingHom.{u3, u5} S W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10))) (RingHom.comp.{u3, u2, u5} S Q W (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q _inst_6)) (Semiring.toNonAssocSemiring.{u5} W (CommSemiring.toSemiring.{u5} W _inst_10)) (IsLocalization.map.{u4, u2, u6, u5} P _inst_4 T Q _inst_6 _inst_7 A _inst_9 _inst_8 U W _inst_10 _inst_11 _inst_12 l hl) (IsLocalization.map.{u1, u3, u4, u2} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy)) (IsLocalization.map.{u1, u3, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx)))
+Case conversion may be inaccurate. Consider using '#align is_localization.map_comp_map IsLocalization.map_comp_mapₓ'. -/
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
 theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W]
@@ -633,6 +1063,12 @@ theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSe
       (toLocalizationMap U W) l _ x
 #align is_localization.map_comp_map IsLocalization.map_comp_map
 
+/- warning: is_localization.map_map -> IsLocalization.map_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) g T)) [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u5}} [_inst_9 : CommSemiring.{u5} A] {U : Submonoid.{u5} A (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))))} {W : Type.{u6}} [_inst_10 : CommSemiring.{u6} W] [_inst_11 : Algebra.{u5, u6} A W _inst_9 (CommSemiring.toSemiring.{u6} W _inst_10)] [_inst_12 : IsLocalization.{u5, u6} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))} (hl : LE.le.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Preorder.toLE.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.completeLattice.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))))) T (Submonoid.comap.{u3, u5, max u3 u5} P A (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u5} A (NonAssocSemiring.toMulZeroOneClass.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u3 u5, u3, u5} (RingHom.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)) (RingHom.ringHomClass.{u3, u5} P A (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_9)))) l U)) (x : S), Eq.{succ u6} W (coeFn.{max (succ u4) (succ u6), max (succ u4) (succ u6)} (RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) (fun (_x : RingHom.{u4, u6} Q W (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (Semiring.toNonAssocSemiring.{u6} W (CommSemiring.toSemiring.{u6} W _inst_10))) => Q -> W) 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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u4}} [_inst_4 : CommSemiring.{u4} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))} {T : Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))} {Q : Type.{u3}} [_inst_6 : CommSemiring.{u3} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) M (Submonoid.comap.{u1, u4, max u1 u4} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) g T)) [_inst_7 : Algebra.{u4, u3} P Q _inst_4 (CommSemiring.toSemiring.{u3} Q _inst_6)] [_inst_8 : IsLocalization.{u4, u3} P _inst_4 T Q _inst_6 _inst_7] {A : Type.{u6}} [_inst_9 : CommSemiring.{u6} A] {U : Submonoid.{u6} A (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))))} {W : Type.{u5}} [_inst_10 : CommSemiring.{u5} W] [_inst_11 : Algebra.{u6, u5} A W _inst_9 (CommSemiring.toSemiring.{u5} W _inst_10)] [_inst_12 : IsLocalization.{u6, u5} A _inst_9 U W _inst_10 _inst_11] {l : RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))} (hl : LE.le.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Preorder.toLE.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (PartialOrder.toPreorder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u4} P (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))))))))) T (Submonoid.comap.{u4, u6, max u4 u6} P A (MulZeroOneClass.toMulOneClass.{u4} P (NonAssocSemiring.toMulZeroOneClass.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (MulZeroOneClass.toMulOneClass.{u6} A (NonAssocSemiring.toMulZeroOneClass.{u6} A (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) (RingHomClass.toMonoidHomClass.{max u4 u6, u4, u6} (RingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9))) P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) (RingHom.instRingHomClassRingHom.{u4, u6} P A (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)))) l U)) (x : S), Eq.{succ u5} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) => W) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} Q (CommSemiring.toSemiring.{u3} Q _inst_6))) S (fun (a : S) => (fun 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(CommSemiring.toSemiring.{u5} W _inst_10)))))) (IsLocalization.map.{u1, u2, u6, u5} R _inst_1 M S _inst_2 _inst_3 A _inst_9 _inst_5 U W _inst_10 _inst_11 _inst_12 (RingHom.comp.{u1, u4, u6} R P A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (Semiring.toNonAssocSemiring.{u6} A (CommSemiring.toSemiring.{u6} A _inst_9)) l g) (fun (x : R) (hx : 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 M) => hl (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} P (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u4} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} P (CommSemiring.toSemiring.{u4} P _inst_4)))))) g x) (hy x hx))) x)
+Case conversion may be inaccurate. Consider using '#align is_localization.map_map IsLocalization.map_mapₓ'. -/
 /-- If `comm_semiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
 theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W] [Algebra A W]
@@ -641,6 +1077,12 @@ theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemirin
   rw [← map_comp_map hy hl] <;> rfl
 #align is_localization.map_map IsLocalization.map_map
 
+/- warning: is_localization.map_smul -> IsLocalization.map_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))} {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) 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x))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] {g : RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))} {T : Submonoid.{u1} P (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] (hy : LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))))) M (Submonoid.comap.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) g T)) [_inst_7 : Algebra.{u1, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u1, u4} P _inst_4 T Q _inst_6 _inst_7] (x : S) (z : R), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) (HSMul.hSMul.{u3, u2, u2} R S S (instHSMul.{u3, u2} R S (Algebra.toSMul.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3)) z x)) (HSMul.hSMul.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (instHSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) (Algebra.toSMul.{u1, u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_4 (CommSemiring.toSemiring.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) x) _inst_6) _inst_7)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (RingHom.instRingHomClassRingHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))) g z) (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) _x) (MulHomClass.toFunLike.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u2, u4} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))))) (IsLocalization.map.{u3, u2, u1, u4} R _inst_1 M S _inst_2 _inst_3 P _inst_4 _inst_5 T Q _inst_6 _inst_7 _inst_8 g hy) x))
+Case conversion may be inaccurate. Consider using '#align is_localization.map_smul IsLocalization.map_smulₓ'. -/
 theorem map_smul (x : S) (z : R) : map Q g hy (z • x : S) = g z • map Q g hy x := by
   rw [Algebra.smul_def, Algebra.smul_def, RingHom.map_mul, map_eq]
 #align is_localization.map_smul IsLocalization.map_smul
@@ -649,6 +1091,12 @@ section
 
 variable (S Q)
 
+/- warning: is_localization.ring_equiv_of_ring_equiv -> IsLocalization.ringEquivOfRingEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} (Q : Type.{u4}) [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (h : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))), (Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) h) M) T) -> (RingEquiv.{u2, u4} S Q (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasMul.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))) (Distrib.toHasAdd.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} (Q : Type.{u4}) [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] (h : RingEquiv.{u1, u3} R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))), (Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) h) M) T) -> (RingEquiv.{u2, u4} S Q (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6)))) (Distrib.toAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toAdd.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))))
+Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv IsLocalization.ringEquivOfRingEquivₓ'. -/
 /-- If `S`, `Q` are localizations of `R` and `P` at submonoids `M, T` respectively, an
 isomorphism `j : R ≃+* P` such that `j(M) = T` induces an isomorphism of localizations
 `S ≃+* Q`. -/
@@ -679,18 +1127,36 @@ noncomputable def ringEquivOfRingEquiv (h : R ≃+* P) (H : M.map h.toMonoidHom
 
 end
 
+/- warning: is_localization.ring_equiv_of_ring_equiv_eq_map -> IsLocalization.ringEquivOfRingEquiv_eq_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T), Eq.{max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))) ((fun (a : Sort.{max (succ u2) (succ u4)}) (b : Sort.{max (succ u2) (succ u4)}) [self : HasLiftT.{max (succ u2) (succ u4), max (succ u2) (succ u4)} a b] => self.0) (RingEquiv.{u2, u4} S Q (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S 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(NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))))) j) M) T H)))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommSemiring.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u4, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u4, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u1}} [_inst_6 : CommSemiring.{u1} Q] [_inst_7 : Algebra.{u3, u1} P Q _inst_4 (CommSemiring.toSemiring.{u1} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u1} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R 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_inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) j) (Submonoid.le_comap_of_map_le.{max u4 u3, u4, u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) T (RingHomClass.toRingHom.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquivClass.toRingHomClass.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) j) (le_of_eq.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))))) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (RingHomClass.toRingHom.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquivClass.toRingHomClass.{max u4 u3, u4, u3} (RingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquiv.instRingEquivClassRingEquiv.{u4, u3} R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (Distrib.toAdd.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Distrib.toAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))))) j) M) T H)))
+Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_eq_map IsLocalization.ringEquivOfRingEquiv_eq_mapₓ'. -/
 theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T) :
     (ringEquivOfRingEquiv S Q j H : S →+* Q) =
       map Q (j : R →+* P) (M.le_comap_of_map_le (le_of_eq H)) :=
   rfl
 #align is_localization.ring_equiv_of_ring_equiv_eq_map IsLocalization.ringEquivOfRingEquiv_eq_map
 
+/- warning: is_localization.ring_equiv_of_ring_equiv_eq -> IsLocalization.ringEquivOfRingEquiv_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))} (H : Eq.{succ u3} (Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) j) M) T) (x : R), Eq.{succ u4} Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingEquiv.{u2, u4} S Q (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasMul.{u4} Q (NonUnitalNonAssocSemiring.toDistrib.{u4} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Q (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q _inst_6))))) (Distrib.toHasAdd.{u4} Q 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eqₓ'. -/
 @[simp]
 theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x) :
     ringEquivOfRingEquiv S Q j H ((algebraMap R S) x) = algebraMap P Q (j x) :=
   map_eq _ _
 #align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eq
 
+/- warning: is_localization.ring_equiv_of_ring_equiv_mk' -> IsLocalization.ringEquivOfRingEquiv_mk' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {T : Submonoid.{u3} P (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))} {Q : Type.{u4}} [_inst_6 : CommSemiring.{u4} Q] [_inst_7 : Algebra.{u3, u4} P Q _inst_4 (CommSemiring.toSemiring.{u4} Q _inst_6)] [_inst_8 : IsLocalization.{u3, u4} P _inst_4 T Q _inst_6 _inst_7] {j : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localization.ring_equiv_of_ring_equiv_mk' IsLocalization.ringEquivOfRingEquiv_mk'ₓ'. -/
 theorem ringEquivOfRingEquiv_mk' {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x : R) (y : M) :
     ringEquivOfRingEquiv S Q j H (mk' S x y) =
       mk' Q (j x) ⟨j y, show j y ∈ T from H ▸ Set.mem_image_of_mem j y.2⟩ :=
@@ -707,6 +1173,7 @@ section
 
 variable (M S Q)
 
+#print IsLocalization.algEquiv /-
 /-- If `S`, `Q` are localizations of `R` at the submonoid `M` respectively,
 there is an isomorphism of localizations `S ≃ₐ[R] Q`. -/
 @[simps]
@@ -714,14 +1181,27 @@ noncomputable def algEquiv : S ≃ₐ[R] Q :=
   { ringEquivOfRingEquiv S Q (RingEquiv.refl R) M.map_id with
     commutes' := ringEquivOfRingEquiv_eq _ }
 #align is_localization.alg_equiv IsLocalization.algEquiv
+-/
 
 end
 
+/- warning: is_localization.alg_equiv_mk' -> IsLocalization.algEquiv_mk' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
   map_mk' _ _ _
 #align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'
 
+/- warning: is_localization.alg_equiv_symm_mk' -> IsLocalization.algEquiv_symm_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_localization.alg_equiv_symm_mk' IsLocalization.algEquiv_symm_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) = mk' S x y :=
   map_mk' _ _ _
@@ -735,6 +1215,12 @@ section
 
 variable (M)
 
+/- warning: is_localization.is_localization_of_alg_equiv -> IsLocalization.isLocalization_of_algEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : Algebra.{u1, u3} R P _inst_1 (CommSemiring.toSemiring.{u3} P _inst_4)] [_inst_6 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], (AlgEquiv.{u1, u2, u3} R S P _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u3} P _inst_4) _inst_3 _inst_5) -> (IsLocalization.{u1, u3} R _inst_1 M P _inst_4 _inst_5)
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : Algebra.{u3, u2} R P _inst_1 (CommSemiring.toSemiring.{u2} P _inst_4)] [_inst_6 : IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3], (AlgEquiv.{u3, u1, u2} R S P _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} P _inst_4) _inst_3 _inst_5) -> (IsLocalization.{u3, u2} R _inst_1 M P _inst_4 _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_localization.is_localization_of_alg_equiv IsLocalization.isLocalization_of_algEquivₓ'. -/
 theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃ₐ[R] P) :
     IsLocalization M P := by
   constructor
@@ -752,11 +1238,23 @@ theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃
     rfl
 #align is_localization.is_localization_of_alg_equiv IsLocalization.isLocalization_of_algEquiv
 
+/- warning: is_localization.is_localization_iff_of_alg_equiv -> IsLocalization.isLocalization_iff_of_algEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : Algebra.{u1, u3} R P _inst_1 (CommSemiring.toSemiring.{u3} P _inst_4)], (AlgEquiv.{u1, u2, u3} R S P _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u3} P _inst_4) _inst_3 _inst_5) -> (Iff (IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3) (IsLocalization.{u1, u3} R _inst_1 M P _inst_4 _inst_5))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] [_inst_5 : Algebra.{u3, u2} R P _inst_1 (CommSemiring.toSemiring.{u2} P _inst_4)], (AlgEquiv.{u3, u1, u2} R S P _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} P _inst_4) _inst_3 _inst_5) -> (Iff (IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3) (IsLocalization.{u3, u2} R _inst_1 M P _inst_4 _inst_5))
+Case conversion may be inaccurate. Consider using '#align is_localization.is_localization_iff_of_alg_equiv IsLocalization.isLocalization_iff_of_algEquivₓ'. -/
 theorem isLocalization_iff_of_algEquiv [Algebra R P] (h : S ≃ₐ[R] P) :
     IsLocalization M S ↔ IsLocalization M P :=
   ⟨fun _ => is_localization_of_alg_equiv M h, fun _ => is_localization_of_alg_equiv M h.symm⟩
 #align is_localization.is_localization_iff_of_alg_equiv IsLocalization.isLocalization_iff_of_algEquiv
 
+/- warning: is_localization.is_localization_iff_of_ring_equiv -> IsLocalization.isLocalization_iff_of_ringEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] (h : RingEquiv.{u2, u3} S P (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))), Iff (IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3) (IsLocalization.{u1, u3} R _inst_1 M P _inst_4 (RingHom.toAlgebra.{u1, u3} R P _inst_1 _inst_4 (RingHom.comp.{u1, u2, u3} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (RingEquiv.toRingHom.{u2, u3} S P (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) h) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) {S : Type.{u3}} [_inst_2 : CommSemiring.{u3} S] [_inst_3 : Algebra.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] (h : RingEquiv.{u3, u2} S P (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))))) (Distrib.toAdd.{u2} P (NonUnitalNonAssocSemiring.toDistrib.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))), Iff (IsLocalization.{u1, u3} R _inst_1 M S _inst_2 _inst_3) (IsLocalization.{u1, u2} R _inst_1 M P _inst_4 (RingHom.toAlgebra.{u1, u2} R P _inst_1 _inst_4 (RingHom.comp.{u1, u3, u2} R S P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (RingEquiv.toRingHom.{u3, u2} S P (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) h) (algebraMap.{u1, u3} R S _inst_1 (CommSemiring.toSemiring.{u3} S _inst_2) _inst_3))))
+Case conversion may be inaccurate. Consider using '#align is_localization.is_localization_iff_of_ring_equiv IsLocalization.isLocalization_iff_of_ringEquivₓ'. -/
 theorem isLocalization_iff_of_ringEquiv (h : S ≃+* P) :
     IsLocalization M S ↔ @IsLocalization _ M P _ (h.toRingHom.comp <| algebraMap R S).toAlgebra :=
   letI := (h.to_ring_hom.comp <| algebraMap R S).toAlgebra
@@ -765,6 +1263,12 @@ theorem isLocalization_iff_of_ringEquiv (h : S ≃+* P) :
 
 variable (S)
 
+/- warning: is_localization.is_localization_of_base_ring_equiv -> IsLocalization.isLocalization_of_base_ringEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (h : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))), IsLocalization.{u3, u2} P _inst_4 (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) h) M) S _inst_2 (RingHom.toAlgebra.{u3, u2} P S _inst_4 _inst_2 (RingHom.comp.{u3, u1, u2} P R S (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (RingEquiv.toRingHom.{u3, u1} P R (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingEquiv.symm.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) h))))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u1}} [_inst_4 : CommSemiring.{u1} P] [_inst_5 : IsLocalization.{u3, u2} R _inst_1 M S _inst_2 _inst_3] (h : RingEquiv.{u3, u1} R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (Distrib.toAdd.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Distrib.toAdd.{u1} P (NonUnitalNonAssocSemiring.toDistrib.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))))), IsLocalization.{u1, u2} P _inst_4 (Submonoid.map.{u3, u1, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (MonoidHom.{u3, u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))) (MonoidHom.monoidHomClass.{u3, u1} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} P (NonAssocSemiring.toMulZeroOneClass.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))) (RingEquiv.toMonoidHom.{u3, u1} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) h) M) S _inst_2 (RingHom.toAlgebra.{u1, u2} P S _inst_4 _inst_2 (RingHom.comp.{u1, u3, u2} P R S (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (algebraMap.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (RingEquiv.toRingHom.{u1, u3} P R (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingEquiv.symm.{u3, u1} R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4)))) (Distrib.toAdd.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Distrib.toAdd.{u1} P (NonUnitalNonAssocSemiring.toDistrib.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P _inst_4))))) h))))
+Case conversion may be inaccurate. Consider using '#align is_localization.is_localization_of_base_ring_equiv IsLocalization.isLocalization_of_base_ringEquivₓ'. -/
 theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
     @IsLocalization _ (M.map h.toMonoidHom) S _
       ((algebraMap R S).comp h.symm.toRingHom).toAlgebra :=
@@ -789,6 +1293,12 @@ theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
       ⟨fun ⟨c, e⟩ => ⟨⟨_, _, c.Prop, rfl⟩, e⟩, fun ⟨⟨_, c, h, e₁⟩, e₂⟩ => ⟨⟨_, h⟩, e₁.symm ▸ e₂⟩⟩
 #align is_localization.is_localization_of_base_ring_equiv IsLocalization.isLocalization_of_base_ringEquiv
 
+/- warning: is_localization.is_localization_iff_of_base_ring_equiv -> IsLocalization.isLocalization_iff_of_base_ringEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] {P : Type.{u3}} [_inst_4 : CommSemiring.{u3} P] (h : RingEquiv.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))))), Iff (IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3) (IsLocalization.{u3, u2} P _inst_4 (Submonoid.map.{u1, u3, max u3 u1} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)))) (MonoidHom.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (MonoidHom.monoidHomClass.{u1, u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (RingEquiv.toMonoidHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) h) M) S _inst_2 (RingHom.toAlgebra.{u3, u2} P S _inst_4 _inst_2 (RingHom.comp.{u3, u1, u2} P R S (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (RingEquiv.toRingHom.{u3, u1} P R (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingEquiv.symm.{u1, u3} R P (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasMul.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) (Distrib.toHasAdd.{u3} P (NonUnitalNonAssocSemiring.toDistrib.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P _inst_4))))) h)))))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (M : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] {P : Type.{u2}} [_inst_4 : CommSemiring.{u2} P] (h : RingEquiv.{u3, u2} R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Distrib.toAdd.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Distrib.toAdd.{u2} P (NonUnitalNonAssocSemiring.toDistrib.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))))), Iff (IsLocalization.{u3, u1} R _inst_1 M S _inst_2 _inst_3) (IsLocalization.{u2, u1} P _inst_4 (Submonoid.map.{u3, u2, max u3 u2} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (MonoidHom.{u3, u2} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (MonoidHom.monoidHomClass.{u3, u2} R P (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} P (NonAssocSemiring.toMulZeroOneClass.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) (RingEquiv.toMonoidHom.{u3, u2} R P (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) h) M) S _inst_2 (RingHom.toAlgebra.{u2, u1} P S _inst_4 _inst_2 (RingHom.comp.{u2, u3, u1} P R S (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (algebraMap.{u3, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (RingEquiv.toRingHom.{u2, u3} P R (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingEquiv.symm.{u3, u2} R P (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4)))) (Distrib.toAdd.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Distrib.toAdd.{u2} P (NonUnitalNonAssocSemiring.toDistrib.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P _inst_4))))) h)))))
+Case conversion may be inaccurate. Consider using '#align is_localization.is_localization_iff_of_base_ring_equiv IsLocalization.isLocalization_iff_of_base_ringEquivₓ'. -/
 theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
     IsLocalization M S ↔
       @IsLocalization _ (M.map h.toMonoidHom) S _
@@ -813,6 +1323,12 @@ variable (M S)
 
 include M
 
+/- warning: is_localization.non_zero_divisors_le_comap -> IsLocalization.nonZeroDivisors_le_comap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Submonoid.comap.{u1, u2, max u1 u2} R S (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (nonZeroDivisors.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3], LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} S (MonoidWithZero.toMulZeroOneClass.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (nonZeroDivisors.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))
+Case conversion may be inaccurate. Consider using '#align is_localization.non_zero_divisors_le_comap IsLocalization.nonZeroDivisors_le_comapₓ'. -/
 theorem nonZeroDivisors_le_comap [IsLocalization M S] :
     nonZeroDivisors R ≤ (nonZeroDivisors S).comap (algebraMap R S) :=
   by
@@ -826,6 +1342,12 @@ theorem nonZeroDivisors_le_comap [IsLocalization M S] :
   exact ⟨c, ha _ e⟩
 #align is_localization.non_zero_divisors_le_comap IsLocalization.nonZeroDivisors_le_comap
 
+/- warning: is_localization.map_non_zero_divisors_le -> IsLocalization.map_nonZeroDivisors_le 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_localization.map_non_zero_divisors_le IsLocalization.map_nonZeroDivisors_leₓ'. -/
 theorem map_nonZeroDivisors_le [IsLocalization M S] :
     (nonZeroDivisors R).map (algebraMap R S) ≤ nonZeroDivisors S :=
   Submonoid.map_le_iff_le_comap.mpr (nonZeroDivisors_le_comap M S)
@@ -847,6 +1369,7 @@ section
 instance [Subsingleton R] : Unique (Localization M) :=
   ⟨⟨1⟩, by intro a; induction a; induction default; congr ; rfl; rfl⟩
 
+#print Localization.add /-
 /-- Addition in a ring localization is defined as `⟨a, b⟩ + ⟨c, d⟩ = ⟨b * c + d * a, b * d⟩`.
 
 Should not be confused with `add_localization.add`, which is defined as
@@ -869,16 +1392,29 @@ protected irreducible_def add (z w : Localization M) : Localization M :=
           _ = t₅ * t₆ * (b * d * (b' * c' + d' * a')) := by rw [ht₆, ht₅] <;> ring
           )
 #align localization.add Localization.add
+-/
 
 instance : Add (Localization M) :=
   ⟨Localization.add⟩
 
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+Case conversion may be inaccurate. Consider using '#align localization.add_mk Localization.add_mkₓ'. -/
 theorem add_mk (a b c d) : (mk a b : Localization M) + mk c d = mk (b * c + d * a) (b * d) :=
   by
   unfold Add.add Localization.add
   apply lift_on₂_mk
 #align localization.add_mk Localization.add_mk
 
+/- warning: localization.add_mk_self -> Localization.add_mk_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localization.add_mk_self Localization.add_mk_selfₓ'. -/
 theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b :=
   by
   rw [add_mk, mk_eq_mk_iff, r_eq_r']
@@ -941,6 +1477,12 @@ instance : CommSemiring (Localization M) :=
           run_tac
             tac) }
 
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+Case conversion may be inaccurate. Consider using '#align localization.mk_add_monoid_hom Localization.mkAddMonoidHomₓ'. -/
 /-- For any given denominator `b : M`, the map `a ↦ a / b` is an `add_monoid_hom` from `R` to
   `localization M`-/
 @[simps]
@@ -951,15 +1493,33 @@ def mkAddMonoidHom (b : M) : R →+ Localization M
   map_add' x y := (add_mk_self _ _ _).symm
 #align localization.mk_add_monoid_hom Localization.mkAddMonoidHom
 
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+Case conversion may be inaccurate. Consider using '#align localization.mk_sum Localization.mk_sumₓ'. -/
 theorem mk_sum {ι : Type _} (f : ι → R) (s : Finset ι) (b : M) :
     mk (∑ i in s, f i) b = ∑ i in s, mk (f i) b :=
   (mkAddMonoidHom b).map_sum f s
 #align localization.mk_sum Localization.mk_sum
 
+/- warning: localization.mk_list_sum -> Localization.mk_list_sum is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localization.mk_list_sum Localization.mk_list_sumₓ'. -/
 theorem mk_list_sum (l : List R) (b : M) : mk l.Sum b = (l.map fun a => mk a b).Sum :=
   (mkAddMonoidHom b).map_list_sum l
 #align localization.mk_list_sum Localization.mk_list_sum
 
+/- warning: localization.mk_multiset_sum -> Localization.mk_multiset_sum is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localization.mk_multiset_sum Localization.mk_multiset_sumₓ'. -/
 theorem mk_multiset_sum (l : Multiset R) (b : M) : mk l.Sum b = (l.map fun a => mk a b).Sum :=
   (mkAddMonoidHom b).map_multiset_sum l
 #align localization.mk_multiset_sum Localization.mk_multiset_sum
@@ -1026,33 +1586,75 @@ instance : IsLocalization M (Localization M)
 
 end
 
+/- warning: localization.to_localization_map_eq_monoid_of -> Localization.toLocalizationMap_eq_monoidOf is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localization.to_localization_map_eq_monoid_of Localization.toLocalizationMap_eq_monoidOfₓ'. -/
 @[simp]
 theorem toLocalizationMap_eq_monoidOf : toLocalizationMap M (Localization M) = monoidOf M :=
   rfl
 #align localization.to_localization_map_eq_monoid_of Localization.toLocalizationMap_eq_monoidOf
 
+/- warning: localization.monoid_of_eq_algebra_map -> Localization.monoidOf_eq_algebraMap 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 localization.monoid_of_eq_algebra_map Localization.monoidOf_eq_algebraMapₓ'. -/
 theorem monoidOf_eq_algebraMap (x) : (monoidOf M).toMap x = algebraMap R (Localization M) x :=
   rfl
 #align localization.monoid_of_eq_algebra_map Localization.monoidOf_eq_algebraMap
 
+/- warning: localization.mk_one_eq_algebra_map -> Localization.mk_one_eq_algebraMap is a dubious translation:
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 theorem mk_one_eq_algebraMap (x) : mk x 1 = algebraMap R (Localization M) x :=
   rfl
 #align localization.mk_one_eq_algebra_map Localization.mk_one_eq_algebraMap
 
+/- warning: localization.mk_eq_mk'_apply -> Localization.mk_eq_mk'_apply is a dubious translation:
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 theorem mk_eq_mk'_apply (x y) : mk x y = IsLocalization.mk' (Localization M) x y := by
   rw [mk_eq_monoid_of_mk'_apply, mk', to_localization_map_eq_monoid_of]
 #align localization.mk_eq_mk'_apply Localization.mk_eq_mk'_apply
 
+/- warning: localization.mk_eq_mk' -> Localization.mk_eq_mk' is a dubious translation:
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 @[simp]
 theorem mk_eq_mk' : (mk : R → M → Localization M) = IsLocalization.mk' (Localization M) :=
   mk_eq_monoidOf_mk'
 #align localization.mk_eq_mk' Localization.mk_eq_mk'
 
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+Case conversion may be inaccurate. Consider using '#align localization.mk_algebra_map Localization.mk_algebraMapₓ'. -/
 theorem mk_algebraMap {A : Type _} [CommSemiring A] [Algebra A R] (m : A) :
     mk (algebraMap A R m) 1 = algebraMap A (Localization M) m := by
   rw [mk_eq_mk', mk'_eq_iff_eq_mul, Submonoid.coe_one, map_one, mul_one] <;> rfl
 #align localization.mk_algebra_map Localization.mk_algebraMap
 
+/- warning: localization.mk_nat_cast -> Localization.mk_nat_cast is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align localization.mk_nat_cast Localization.mk_nat_castₓ'. -/
 theorem mk_nat_cast (m : ℕ) : (mk m 1 : Localization M) = m := by
   simpa using @mk_algebra_map R _ M ℕ _ _ m
 #align localization.mk_nat_cast Localization.mk_nat_cast
@@ -1063,35 +1665,67 @@ section
 
 variable (M S)
 
+/- warning: localization.alg_equiv -> Localization.algEquiv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localization.alg_equiv Localization.algEquivₓ'. -/
 /-- The localization of `R` at `M` as a quotient type is isomorphic to any other localization. -/
 @[simps]
 noncomputable def algEquiv : Localization M ≃ₐ[R] S :=
   IsLocalization.algEquiv M _ _
 #align localization.alg_equiv Localization.algEquiv
 
+#print IsLocalization.unique /-
 /-- The localization of a singleton is a singleton. Cannot be an instance due to metavariables. -/
 noncomputable def IsLocalization.unique (R Rₘ) [CommSemiring R] [CommSemiring Rₘ] (M : Submonoid R)
     [Subsingleton R] [Algebra R Rₘ] [IsLocalization M Rₘ] : Unique Rₘ :=
   have : Inhabited Rₘ := ⟨1⟩
   (AlgEquiv M Rₘ).symm.Injective.unique
 #align is_localization.unique IsLocalization.unique
+-/
 
 end
 
+/- warning: localization.alg_equiv_mk' -> Localization.algEquiv_mk' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_mk' Localization.algEquiv_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) = mk' S x y :=
   algEquiv_mk' _ _
 #align localization.alg_equiv_mk' Localization.algEquiv_mk'
 
+/- warning: localization.alg_equiv_symm_mk' -> Localization.algEquiv_symm_mk' is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (SMulZeroClass.toSMul.{u2, 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 _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, 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 _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3))))) (SMulZeroClass.toSMul.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toZero.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddCommMonoid.toAddMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AddMonoid.toAddZeroClass.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) 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(CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, u1, u2} (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 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(CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)))))) (Module.toDistribMulAction.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Algebra.toModule.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3)) (Module.toDistribMulAction.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Semiring.toNonAssocSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M))))) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (AlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) 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u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Algebra.toModule.{u2, u2} R (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHomClass.linearMapClass.{u2, u1, u2, max u2 u1} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} 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(Algebra.id.{u2} R _inst_1))) R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u1, u2} R S (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) (CommSemiring.toSemiring.{u2} (Localization.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u2} R _inst_1 M)) _inst_3 (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u2, u2} R _inst_1 M R _inst_1 (Algebra.id.{u2} R 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+Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_symm_mk' Localization.algEquiv_symm_mk'ₓ'. -/
 @[simp]
 theorem algEquiv_symm_mk' (x : R) (y : M) :
     (algEquiv M S).symm (mk' S x y) = mk' (Localization M) x y :=
   algEquiv_symm_mk' _ _
 #align localization.alg_equiv_symm_mk' Localization.algEquiv_symm_mk'
 
+/- warning: localization.alg_equiv_mk -> Localization.algEquiv_mk is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))) M), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgEquiv.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) => (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) -> S) (AlgEquiv.hasCoeToFun.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3) (Localization.algEquiv.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x y)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))} (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_5 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R (CommMonoid.toMonoid.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R (CommMonoid.toMonoid.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R (CommMonoid.toMonoid.{u2} R (CommSemiring.toCommMonoid.{u2} R _inst_1))))) x M)), Eq.{succ u1} ((fun 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+Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_mk Localization.algEquiv_mkₓ'. -/
 theorem algEquiv_mk (x y) : algEquiv M S (mk x y) = mk' S x y := by rw [mk_eq_mk', alg_equiv_mk']
 #align localization.alg_equiv_mk Localization.algEquiv_mk
 
+/- warning: localization.alg_equiv_symm_mk -> Localization.algEquiv_symm_mk is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))} {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_5 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (x : R) (y : 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)))))) M), Eq.{succ u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgEquiv.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) (fun (_x : AlgEquiv.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) => S -> (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M)) (AlgEquiv.hasCoeToFun.{u1, u2, u1} R S (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) _inst_3 (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.symm.{u1, u1, u2} R (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) S _inst_1 (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M) (Localization.commSemiring.{u1} R _inst_1 M)) (CommSemiring.toSemiring.{u2} S _inst_2) (Localization.algebra.{u1, u1} R _inst_1 M R _inst_1 (Algebra.id.{u1} R _inst_1)) _inst_3 (Localization.algEquiv.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5)) (IsLocalization.mk'.{u1, u2} R _inst_1 M S _inst_2 _inst_3 _inst_5 x y)) (Localization.mk.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1) M x y)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align localization.alg_equiv_symm_mk Localization.algEquiv_symm_mkₓ'. -/
 theorem algEquiv_symm_mk (x : R) (y : M) : (algEquiv M S).symm (mk' S x y) = mk x y := by
   rw [mk_eq_mk', alg_equiv_symm_mk']
 #align localization.alg_equiv_symm_mk Localization.algEquiv_symm_mk
@@ -1108,6 +1742,7 @@ variable [Algebra R S] {P : Type _} [CommRing P]
 
 namespace Localization
 
+#print Localization.neg /-
 /-- Negation in a ring localization is defined as `-⟨a, b⟩ = ⟨-a, b⟩`. -/
 protected irreducible_def neg (z : Localization M) : Localization M :=
   Localization.liftOn z (fun a b => mk (-a) b) fun a b c d h =>
@@ -1119,10 +1754,17 @@ protected irreducible_def neg (z : Localization M) : Localization M :=
         rw [mul_neg, mul_neg, ht]
         ring_nf)
 #align localization.neg Localization.neg
+-/
 
 instance : Neg (Localization M) :=
   ⟨Localization.neg⟩
 
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+Case conversion may be inaccurate. Consider using '#align localization.neg_mk Localization.neg_mkₓ'. -/
 theorem neg_mk (a b) : -(mk a b : Localization M) = mk (-a) b :=
   by
   unfold Neg.neg Localization.neg
@@ -1154,6 +1796,12 @@ instance : CommRing (Localization M) :=
           simp only [Submonoid.coe_mul]
           ring) }
 
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+Case conversion may be inaccurate. Consider using '#align localization.sub_mk Localization.sub_mkₓ'. -/
 theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b * c) (b * d) :=
   calc
     mk a b - mk c d = mk a b + -mk c d := sub_eq_add_neg _ _
@@ -1163,6 +1811,12 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b
     
 #align localization.sub_mk Localization.sub_mk
 
+/- warning: localization.mk_int_cast -> Localization.mk_int_cast is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align localization.mk_int_cast Localization.mk_int_castₓ'. -/
 theorem mk_int_cast (m : ℤ) : (mk m 1 : Localization M) = m := by
   simpa using @mk_algebra_map R _ M ℤ _ _ m
 #align localization.mk_int_cast Localization.mk_int_cast
@@ -1173,6 +1827,12 @@ namespace IsLocalization
 
 variable {R M} (S) {K : Type _} [IsLocalization M S]
 
+/- warning: is_localization.to_map_eq_zero_iff -> IsLocalization.to_map_eq_zero_iff is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {x : R}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Iff (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))))
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+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] {x : R}, (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))))) (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iffₓ'. -/
 theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R S x = 0 ↔ x = 0 :=
   by
   rw [← (algebraMap R S).map_zero]
@@ -1183,6 +1843,12 @@ theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R
   · rw [h]
 #align is_localization.to_map_eq_zero_iff IsLocalization.to_map_eq_zero_iff
 
+/- warning: is_localization.injective -> IsLocalization.injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (Function.Injective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align is_localization.injective IsLocalization.injectiveₓ'. -/
 protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraMap R S) :=
   by
   rw [injective_iff_map_eq_zero (algebraMap R S)]
@@ -1190,6 +1856,12 @@ protected theorem injective (hM : M ≤ nonZeroDivisors R) : Injective (algebraM
   rwa [to_map_eq_zero_iff S hM] at ha
 #align is_localization.injective IsLocalization.injective
 
+/- warning: is_localization.to_map_ne_zero_of_mem_non_zero_divisors -> IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisors is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{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 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {x : R}, (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) 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_2)))))))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))))))
+Case conversion may be inaccurate. Consider using '#align is_localization.to_map_ne_zero_of_mem_non_zero_divisors IsLocalization.to_map_ne_zero_of_mem_nonZeroDivisorsₓ'. -/
 protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M ≤ nonZeroDivisors R)
     {x : R} (hx : x ∈ nonZeroDivisors R) : algebraMap R S x ≠ 0 :=
   show (algebraMap R S).toMonoidWithZeroHom x ≠ 0 from
@@ -1198,11 +1870,23 @@ protected theorem to_map_ne_zero_of_mem_nonZeroDivisors [Nontrivial R] (hM : M 
 
 variable {S}
 
+/- warning: is_localization.sec_snd_ne_zero -> IsLocalization.sec_snd_ne_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_localization.sec_snd_ne_zero IsLocalization.sec_snd_ne_zeroₓ'. -/
 theorem sec_snd_ne_zero [Nontrivial R] (hM : M ≤ nonZeroDivisors R) (x : S) :
     ((sec M x).snd : R) ≠ 0 :=
   nonZeroDivisors.coe_ne_zero ⟨(sec M x).snd.val, hM (sec M x).snd.property⟩
 #align is_localization.sec_snd_ne_zero IsLocalization.sec_snd_ne_zero
 
+/- warning: is_localization.sec_fst_ne_zero -> IsLocalization.sec_fst_ne_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_6 : Nontrivial.{u2} R] [_inst_7 : NoZeroDivisors.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (forall {x : S}, (Ne.{succ u1} S x (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) -> (Ne.{succ u2} R (Prod.fst.{u2, u2} R (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 M)) (IsLocalization.sec.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 _inst_5 x)) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zeroₓ'. -/
 theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDivisors R) {x : S}
     (hx : x ≠ 0) : (sec M x).fst ≠ 0 :=
   by
@@ -1215,6 +1899,12 @@ theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDiv
 
 variable (S M) (Q : Type _) [CommRing Q] {g : R →+* P} [Algebra P Q]
 
+/- warning: is_localization.map_injective_of_injective -> IsLocalization.map_injective_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] (Q : Type.{u4}) [_inst_6 : CommRing.{u4} Q] {g : RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u4} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (Ring.toSemiring.{u4} Q (CommRing.toRing.{u4} Q _inst_6))], (Function.Injective.{succ u1, succ u3} R P (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (fun (_x : RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) => R -> P) (RingHom.hasCoeToFun.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u4} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7], Function.Injective.{succ u2, succ u4} S Q (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (fun (_x : RingHom.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) => S -> Q) (RingHom.hasCoeToFun.{u2, u4} S Q (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u4} Q (CommSemiring.toSemiring.{u4} Q (CommRing.toCommSemiring.{u4} Q _inst_6)))) (IsLocalization.map.{u1, u2, u3, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u4} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{u1, u3, max u1 u3} R P (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.ringHomClass.{u1, u3} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] (M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {P : Type.{u3}} [_inst_4 : CommRing.{u3} P] [_inst_5 : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] (Q : Type.{u2}) [_inst_6 : CommRing.{u2} Q] {g : RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))} [_inst_7 : Algebra.{u3, u2} P Q (CommRing.toCommSemiring.{u3} P _inst_4) (Ring.toSemiring.{u2} Q (CommRing.toRing.{u2} Q _inst_6))], (Function.Injective.{succ u4, succ u3} R P (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => P) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))))) g)) -> (forall [_inst_8 : IsLocalization.{u3, u2} P (CommRing.toCommSemiring.{u3} P _inst_4) (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7], Function.Injective.{succ u1, succ u2} S Q (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => Q) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u2} Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Q (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6)))) S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))) (RingHom.instRingHomClassRingHom.{u1, u2} S Q (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u2} Q (CommSemiring.toSemiring.{u2} Q (CommRing.toCommSemiring.{u2} Q _inst_6))))))) (IsLocalization.map.{u4, u1, u3, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3 P (CommRing.toCommSemiring.{u3} P _inst_4) _inst_5 (Submonoid.map.{u4, u3, max u4 u3} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4)))) R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} P (Ring.toNonAssocRing.{u3} P (CommRing.toRing.{u3} P _inst_4))))) g M) Q (CommRing.toCommSemiring.{u2} Q _inst_6) _inst_7 _inst_8 g (Submonoid.le_comap_map.{max u4 u3, u3, u4} R P (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u3} P (NonAssocSemiring.toMulZeroOneClass.{u3} P (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) M (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) (RingHomClass.toMonoidHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4)))) R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))) (RingHom.instRingHomClassRingHom.{u4, u3} R P (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} P (CommSemiring.toSemiring.{u3} P (CommRing.toCommSemiring.{u3} P _inst_4))))) g))))
+Case conversion may be inaccurate. Consider using '#align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injectiveₓ'. -/
 /-- Injectivity of a map descends to the map induced on localizations. -/
 theorem map_injective_of_injective (hg : Function.Injective g)
     [IsLocalization (M.map g : Submonoid P) Q] :
@@ -1236,6 +1926,12 @@ variable {S Q M}
 
 variable (A : Type _) [CommRing A] [IsDomain A]
 
+/- warning: is_localization.no_zero_divisors_of_le_non_zero_divisors -> IsLocalization.noZeroDivisors_of_le_nonZeroDivisors is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.completeLattice.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (NoZeroDivisors.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2))) (MulZeroClass.toHasZero.{u1} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))
+but is expected to have type
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (NoZeroDivisors.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))
+Case conversion may be inaccurate. Consider using '#align is_localization.no_zero_divisors_of_le_non_zero_divisors IsLocalization.noZeroDivisors_of_le_nonZeroDivisorsₓ'. -/
 /-- A `comm_ring` `S` which is the localization of a ring `R` without zero divisors at a subset of
 non-zero elements does not have zero divisors.
 See note [reducible non-instances]. -/
@@ -1256,6 +1952,12 @@ theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [Is
       · exact Or.inr (eq_zero_of_fst_eq_zero hy H) }
 #align is_localization.no_zero_divisors_of_le_non_zero_divisors IsLocalization.noZeroDivisors_of_le_nonZeroDivisors
 
+/- warning: is_localization.is_domain_of_le_non_zero_divisors -> IsLocalization.isDomain_of_le_nonZeroDivisors is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.completeLattice.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))
+but is expected to have type
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (A : Type.{u2}) [_inst_8 : CommRing.{u2} A] [_inst_9 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))] [_inst_10 : Algebra.{u2, u1} A S (CommRing.toCommSemiring.{u2} A _inst_8) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] {M : Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))} [_inst_11 : IsLocalization.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_8) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_10], (LE.le.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Preorder.toLE.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_8)))))))))) M (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_8))))) -> (IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))
+Case conversion may be inaccurate. Consider using '#align is_localization.is_domain_of_le_non_zero_divisors IsLocalization.isDomain_of_le_nonZeroDivisorsₓ'. -/
 /-- A `comm_ring` `S` which is the localization of an integral domain `R` at a subset of
 non-zero elements is an integral domain.
 See note [reducible non-instances]. -/
@@ -1273,6 +1975,12 @@ theorem isDomain_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [IsLocali
 
 variable {A}
 
+/- warning: is_localization.is_domain_localization -> IsLocalization.isDomain_localization is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_8 : CommRing.{u1} A] [_inst_9 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))] {M : Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))}, (LE.le.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Preorder.toLE.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Submonoid.completeLattice.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))))))) M (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))))) -> (IsDomain.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Ring.toSemiring.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (CommRing.toRing.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Localization.commRing.{u1} A _inst_8 M))))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_8 : CommRing.{u1} A] [_inst_9 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))] {M : Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))}, (LE.le.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Preorder.toLE.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_8)))))))))) M (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_8))))) -> (IsDomain.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Ring.toSemiring.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (CommRing.toRing.{u1} (Localization.{u1} A (CommRing.toCommMonoid.{u1} A _inst_8) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} A _inst_8 M))))
+Case conversion may be inaccurate. Consider using '#align is_localization.is_domain_localization IsLocalization.isDomain_localizationₓ'. -/
 /-- The localization at of an integral domain to a set of non-zero elements is an integral domain.
 See note [reducible non-instances]. -/
 @[reducible]
@@ -1285,6 +1993,12 @@ end IsLocalization
 
 open IsLocalization
 
+/- warning: is_field.localization_map_bijective -> IsField.localization_map_bijective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {Rₘ : Type.{u2}} [_inst_5 : CommRing.{u1} R] [_inst_6 : CommRing.{u2} Rₘ] {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_5)))))}, (Not (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_5)))))) (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_5)))))) 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_5))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))))) M)) -> (IsField.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) -> (forall [_inst_7 : Algebra.{u1, u2} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u1, succ u2} R Rₘ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) (fun (_x : RingHom.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) => R -> Rₘ) (RingHom.hasCoeToFun.{u1, u2} R Rₘ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toNonAssocSemiring.{u2} Rₘ (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)))) (algebraMap.{u1, u2} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_6)) _inst_7)))
+but is expected to have type
+  forall {R : Type.{u2}} {Rₘ : Type.{u1}} [_inst_5 : CommRing.{u2} R] [_inst_6 : CommRing.{u1} Rₘ] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))}, (Not (Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) M)) -> (IsField.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5))) -> (forall [_inst_7 : Algebra.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_5) M Rₘ (CommRing.toCommSemiring.{u1} Rₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} R Rₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Rₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Rₘ (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)))) R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} R Rₘ (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u1} Rₘ (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6))))))) (algebraMap.{u2, u1} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u1} Rₘ (CommRing.toRing.{u1} Rₘ _inst_6)) _inst_7)))
+Case conversion may be inaccurate. Consider using '#align is_field.localization_map_bijective IsField.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommRing Rₘ]
     {M : Submonoid R} (hM : (0 : R) ∉ M) (hR : IsField R) [Algebra R Rₘ] [IsLocalization M Rₘ] :
@@ -1298,6 +2012,12 @@ theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommR
   exact ⟨r * n, by erw [eq_mk'_iff_mul_eq, ← map_mul, mul_assoc, mul_comm n, hn, mul_one]⟩
 #align is_field.localization_map_bijective IsField.localization_map_bijective
 
+/- warning: field.localization_map_bijective -> Field.localization_map_bijective is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {Kₘ : Type.{u2}} [_inst_5 : Field.{u1} K] [_inst_6 : CommRing.{u2} Kₘ] {M : Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))}, (Not (Membership.Mem.{u1, u1} K (Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))))) K (Submonoid.setLike.{u1} K (MulZeroOneClass.toMulOneClass.{u1} K (NonAssocSemiring.toMulZeroOneClass.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))))))) M)) -> (forall [_inst_7 : Algebra.{u1, u2} K Kₘ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u1, u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u2} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u1, succ u2} K Kₘ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) (fun (_x : RingHom.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) => K -> Kₘ) (RingHom.hasCoeToFun.{u1, u2} K Kₘ (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (Semiring.toNonAssocSemiring.{u2} Kₘ (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)))) (algebraMap.{u1, u2} K Kₘ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) (Ring.toSemiring.{u2} Kₘ (CommRing.toRing.{u2} Kₘ _inst_6)) _inst_7)))
+but is expected to have type
+  forall {K : Type.{u2}} {Kₘ : Type.{u1}} [_inst_5 : Field.{u2} K] [_inst_6 : CommRing.{u1} Kₘ] {M : Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))}, (Not (Membership.mem.{u2, u2} K (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))) K (Submonoid.instSetLikeSubmonoid.{u2} K (MulZeroOneClass.toMulOneClass.{u2} K (NonAssocSemiring.toMulZeroOneClass.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))))) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) M)) -> (forall [_inst_7 : Algebra.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))] [_inst_8 : IsLocalization.{u2, u1} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) M Kₘ (CommRing.toCommSemiring.{u1} Kₘ _inst_6) _inst_7], Function.Bijective.{succ u2, succ u1} K Kₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : K) => Kₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))))) (NonUnitalNonAssocSemiring.toMul.{u1} Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Kₘ (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)))) K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} K Kₘ (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))) (Semiring.toNonAssocSemiring.{u1} Kₘ (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6))))))) (algebraMap.{u2, u1} K Kₘ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (Ring.toSemiring.{u1} Kₘ (CommRing.toRing.{u1} Kₘ _inst_6)) _inst_7)))
+Case conversion may be inaccurate. Consider using '#align field.localization_map_bijective Field.localization_map_bijectiveₓ'. -/
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
 theorem Field.localization_map_bijective {K Kₘ : Type _} [Field K] [CommRing Kₘ] {M : Submonoid K}
     (hM : (0 : K) ∉ M) [Algebra K Kₘ] [IsLocalization M Kₘ] :
@@ -1319,6 +2039,7 @@ section
 
 variable (S M)
 
+#print localizationAlgebra /-
 /-- Definition of the natural algebra induced by the localization of an algebra.
 Given an algebra `R → S`, a submonoid `R` of `M`, and a localization `Rₘ` for `M`,
 let `Sₘ` be the localization of `S` to the image of `M` under `algebra_map R S`.
@@ -1334,6 +2055,7 @@ noncomputable def localizationAlgebra : Algebra Rₘ Sₘ :=
         (show _ ≤ (Algebra.algebraMapSubmonoid S M).comap _ from M.le_comap_map) :
       Rₘ →+* Sₘ).toAlgebra
 #align localization_algebra localizationAlgebra
+-/
 
 end
 
@@ -1345,12 +2067,24 @@ variable (S Rₘ Sₘ)
 
 include S
 
+/- warning: is_localization.map_units_map_submonoid -> IsLocalization.map_units_map_submonoid is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Sₘ : Type.{u3}) [_inst_6 : CommRing.{u3} Sₘ] [_inst_9 : Algebra.{u2, u3} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u3} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u1, u3} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u1, u2, u3} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} S Sₘ (AddZeroClass.toHasZero.{u3} 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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))} (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] (Sₘ : Type.{u1}) [_inst_6 : CommRing.{u1} Sₘ] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9] [_inst_12 : Algebra.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_14 : IsScalarTower.{u2, u3, u1} R S Sₘ (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3) (Algebra.toSMul.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_12)] (y : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R 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(Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) _inst_12) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) M)) y))
+Case conversion may be inaccurate. Consider using '#align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoidₓ'. -/
 theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R Sₘ y) :=
   by
   rw [IsScalarTower.algebraMap_apply _ S]
   exact IsLocalization.map_units Sₘ ⟨algebraMap R S y, Algebra.mem_algebraMapSubmonoid_of_mem y⟩
 #align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoid
 
+/- warning: is_localization.algebra_map_mk' -> IsLocalization.algebraMap_mk' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : R) (y : 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))))))) M), Eq.{succ u4} Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ 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_inst_10 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u2} S (fun (x : S) => Membership.Mem.{u2, u2} S 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(Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M) 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))))))) M) 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 M))))) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M y)))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))} (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u4, u2, u3} R Rₘ Sₘ (Algebra.toSMul.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u4, u1, u3} R S Sₘ (Algebra.toSMul.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u4, u3} R Sₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] (x : R) (y : Subtype.{succ u4} R (fun (x : R) => Membership.mem.{u4, u4} R (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (SetLike.instMembership.{u4, u4} (Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1))))))) x M)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Sₘ (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))))))) (algebraMap.{u2, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.mk'.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7 _inst_8 x y)) (IsLocalization.mk'.{u1, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2) (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) x) (Subtype.mk.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (fun (x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Submonoid.instSetLikeSubmonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2))))))) x_1 (Algebra.algebraMapSubmonoid.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u1, u4, u1} (RingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u1} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (algebraMap.{u4, u1} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (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 (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) M)) y)) (Algebra.mem_algebraMapSubmonoid_of_mem.{u1, u4} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M y)))
+Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_mk' IsLocalization.algebraMap_mk'ₓ'. -/
 @[simp]
 theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
     algebraMap Rₘ Sₘ (IsLocalization.mk' Rₘ x y) =
@@ -1366,6 +2100,12 @@ theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
 
 variable (M)
 
+/- warning: is_localization.algebra_map_eq_map_map_submonoid -> IsLocalization.algebraMap_eq_map_map_submonoid is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))], Eq.{max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u4}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u4} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Rₘ (CommRing.toRing.{u4} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u4, u3} R Rₘ Sₘ (Algebra.toSMul.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Rₘ (CommRing.toRing.{u4} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u3} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u4} Rₘ (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)))) (algebraMap.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (IsLocalization.map.{u2, u4, u1, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3))]))
+Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_eq_map_map_submonoid IsLocalization.algebraMap_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
 R  →  S
@@ -1382,6 +2122,12 @@ theorem IsLocalization.algebraMap_eq_map_map_submonoid :
       rw [← IsScalarTower.algebraMap_apply R S Sₘ, ← IsScalarTower.algebraMap_apply R Rₘ Sₘ]
 #align is_localization.algebra_map_eq_map_map_submonoid IsLocalization.algebraMap_eq_map_map_submonoid
 
+/- warning: is_localization.algebra_map_apply_eq_map_map_submonoid -> IsLocalization.algebraMap_apply_eq_map_map_submonoid is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] (x : Rₘ), Eq.{succ u4} Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (IsLocalization.map.{u1, u3, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) ((fun (this : LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{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.partialOrder.{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))))))))) M (Submonoid.comap.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{u1, u2, max 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_1))))) (MulZeroOneClass.toMulOneClass.{u2} S (NonAssocSemiring.toMulZeroOneClass.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) M (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))) x)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u4} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u3, u4} R Rₘ Sₘ (Algebra.toSMul.{u2, u3} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u4} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u4} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u4} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)] (x : Rₘ), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11) x) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u3, u4} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6))))))) (IsLocalization.map.{u2, u3, u1, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_8 (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9 _inst_10 (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) ([mdata let_fun:1 (fun (this : LE.le.{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)))))) (Preorder.toLE.{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)))))) (PartialOrder.toPreorder.{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)))))) (OmegaCompletePartialOrder.toPartialOrder.{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)))))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))) (Submonoid.instCompleteLatticeSubmonoid.{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 (Submonoid.comap.{u2, u1, max u2 u1} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M))) => this) (Submonoid.le_comap_map.{max u2 u1, u1, u2} R S (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} S (NonAssocSemiring.toMulZeroOneClass.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) M (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toMonoidHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3))])) x)
+Case conversion may be inaccurate. Consider using '#align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoidₓ'. -/
 /-- If the square below commutes, the bottom map is uniquely specified:
 ```
 R  →  S
@@ -1398,6 +2144,12 @@ theorem IsLocalization.algebraMap_apply_eq_map_map_submonoid (x) :
 
 variable {R}
 
+/- warning: is_localization.lift_algebra_map_eq_algebra_map -> IsLocalization.lift_algebraMap_eq_algebraMap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (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_1)))))) (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_12 : Algebra.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u1, u3, u4} R Rₘ Sₘ (SMulZeroClass.toHasSmul.{u1, u3} R Rₘ (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R Rₘ (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.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R Rₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} Rₘ (AddMonoid.toAddZeroClass.{u3} Rₘ (AddCommMonoid.toAddMonoid.{u3} Rₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R Rₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} Rₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))))) (Algebra.toModule.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u3, u4} Rₘ Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} Rₘ Sₘ (MulZeroClass.toHasZero.{u3} Rₘ (MulZeroOneClass.toMulZeroClass.{u3} Rₘ (MonoidWithZero.toMulZeroOneClass.{u3} Rₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} Rₘ Sₘ (Semiring.toMonoidWithZero.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} Rₘ Sₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))] [_inst_14 : IsScalarTower.{u1, u2, u4} R S Sₘ (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_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} S Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} S Sₘ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} S Sₘ (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} S Sₘ (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_9))))) (SMulZeroClass.toHasSmul.{u1, u4} R Sₘ (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Sₘ (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.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Sₘ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Sₘ (AddMonoid.toAddZeroClass.{u4} Sₘ (AddCommMonoid.toAddMonoid.{u4} Sₘ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Sₘ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Sₘ (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))))) (Algebra.toModule.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12)))))], Eq.{max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (CommSemiring.toSemiring.{u4} Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6)))) (IsLocalization.lift.{u1, u3, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7 Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_8 (algebraMap.{u1, u4} R Sₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_12) (IsLocalization.map_units_map_submonoid.{u1, u2, u4} R _inst_1 M S _inst_2 _inst_3 Sₘ _inst_6 _inst_9 _inst_10 _inst_12 _inst_14)) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) _inst_11)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] (Rₘ : Type.{u4}) (Sₘ : Type.{u3}) [_inst_5 : CommRing.{u4} Rₘ] [_inst_6 : CommRing.{u3} Sₘ] [_inst_7 : Algebra.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Rₘ (CommRing.toRing.{u4} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u2, u4} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u1, u3} S (CommRing.toCommSemiring.{u1} S _inst_2) (Algebra.algebraMapSubmonoid.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_9] [_inst_11 : Algebra.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_12 : Algebra.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6))] [_inst_13 : IsScalarTower.{u2, u4, u3} R Rₘ Sₘ (Algebra.toSMul.{u2, u4} R Rₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} Rₘ (CommRing.toRing.{u4} Rₘ _inst_5)) _inst_7) (Algebra.toSMul.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)] [_inst_14 : IsScalarTower.{u2, u1, u3} R S Sₘ (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u1, u3} S Sₘ (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_9) (Algebra.toSMul.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12)], Eq.{max (succ u4) (succ u3)} (RingHom.{u4, u3} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u4} Rₘ (CommSemiring.toSemiring.{u4} Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u3} Sₘ (CommSemiring.toSemiring.{u3} Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6)))) (IsLocalization.lift.{u2, u4, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) _inst_7 Sₘ (CommRing.toCommSemiring.{u3} Sₘ _inst_6) _inst_8 (algebraMap.{u2, u3} R Sₘ (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_12) (IsLocalization.map_units_map_submonoid.{u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Sₘ _inst_6 _inst_9 _inst_10 _inst_12 _inst_14)) (algebraMap.{u4, u3} Rₘ Sₘ (CommRing.toCommSemiring.{u4} Rₘ _inst_5) (Ring.toSemiring.{u3} Sₘ (CommRing.toRing.{u3} Sₘ _inst_6)) _inst_11)
+Case conversion may be inaccurate. Consider using '#align is_localization.lift_algebra_map_eq_algebra_map IsLocalization.lift_algebraMap_eq_algebraMapₓ'. -/
 theorem IsLocalization.lift_algebraMap_eq_algebraMap :
     @IsLocalization.lift R _ M Rₘ _ _ Sₘ _ _ (algebraMap R Sₘ)
         (IsLocalization.map_units_map_submonoid S Sₘ) =
@@ -1409,6 +2161,12 @@ end
 
 variable (Rₘ Sₘ)
 
+/- warning: localization_algebra_injective -> localizationAlgebra_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {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_1)))))} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (Rₘ : Type.{u3}) (Sₘ : Type.{u4}) [_inst_5 : CommRing.{u3} Rₘ] [_inst_6 : CommRing.{u4} Sₘ] [_inst_7 : Algebra.{u1, u3} R Rₘ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} Rₘ (CommRing.toRing.{u3} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u2, u4} S Sₘ (CommRing.toCommSemiring.{u2} S _inst_2) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u2, u4} S (CommRing.toCommSemiring.{u2} S _inst_2) (Algebra.algebraMapSubmonoid.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u4} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u3, succ u4} Rₘ Sₘ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (fun (_x : RingHom.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) => Rₘ -> Sₘ) (RingHom.hasCoeToFun.{u3, u4} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u3} Rₘ (CommSemiring.toSemiring.{u3} Rₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u4} Sₘ (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)))) (algebraMap.{u3, u4} Rₘ Sₘ (CommRing.toCommSemiring.{u3} Rₘ _inst_5) (Ring.toSemiring.{u4} Sₘ (CommRing.toRing.{u4} Sₘ _inst_6)) (localizationAlgebra.{u1, u2, u3, u4} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {M : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))} {S : Type.{u3}} [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] (Rₘ : Type.{u2}) (Sₘ : Type.{u1}) [_inst_5 : CommRing.{u2} Rₘ] [_inst_6 : CommRing.{u1} Sₘ] [_inst_7 : Algebra.{u4, u2} R Rₘ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₘ (CommRing.toRing.{u2} Rₘ _inst_5))] [_inst_8 : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) M Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) _inst_7] [_inst_9 : Algebra.{u3, u1} S Sₘ (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))] [_inst_10 : IsLocalization.{u3, u1} S (CommRing.toCommSemiring.{u3} S _inst_2) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3 M) Sₘ (CommRing.toCommSemiring.{u1} Sₘ _inst_6) _inst_9], (Function.Injective.{succ u4, succ u3} R S (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (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} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u3} R S (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))))) (algebraMap.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3))) -> (Function.Injective.{succ u2, succ u1} Rₘ Sₘ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ (fun (_x : Rₘ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Rₘ) => Sₘ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonUnitalNonAssocSemiring.toMul.{u2} Rₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Sₘ (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)))) Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u1} Rₘ Sₘ (Semiring.toNonAssocSemiring.{u2} Rₘ (CommSemiring.toSemiring.{u2} Rₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5))) (Semiring.toNonAssocSemiring.{u1} Sₘ (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6))))))) (algebraMap.{u2, u1} Rₘ Sₘ (CommRing.toCommSemiring.{u2} Rₘ _inst_5) (Ring.toSemiring.{u1} Sₘ (CommRing.toRing.{u1} Sₘ _inst_6)) (localizationAlgebra.{u4, u3, u2, u1} R _inst_1 M S _inst_2 _inst_3 Rₘ Sₘ _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10))))
+Case conversion may be inaccurate. Consider using '#align localization_algebra_injective localizationAlgebra_injectiveₓ'. -/
 /-- Injectivity of the underlying `algebra_map` descends to the algebra induced by localization. -/
 theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)) :
     Function.Injective (@algebraMap Rₘ Sₘ _ _ (localizationAlgebra M S)) :=

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

@@ -887,17 +887,17 @@ theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b
   ring
 #align localization.add_mk_self Localization.add_mk_self
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
 private unsafe def tac :=
   sorry
 #align localization.tac localization.tac
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic _private.677500921.tac -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic _private.677500921.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.677500921.tac -/
 instance : CommSemiring (Localization M) :=
   { Localization.commMonoidWithZero M with
     zero := 0
@@ -1158,7 +1158,7 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d = mk (d * a - b
   calc
     mk a b - mk c d = mk a b + -mk c d := sub_eq_add_neg _ _
     _ = mk a b + mk (-c) d := by rw [neg_mk]
-    _ = mk (b * -c + d * a) (b * d) := add_mk _ _ _ _
+    _ = mk (b * -c + d * a) (b * d) := (add_mk _ _ _ _)
     _ = mk (d * a - b * c) (b * d) := by congr <;> ring
     
 #align localization.sub_mk Localization.sub_mk

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

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -1096,9 +1096,9 @@ theorem mk_algebraMap {A : Type*} [CommSemiring A] [Algebra A R] (m : A) :
   rw [mk_eq_mk', mk'_eq_iff_eq_mul, Submonoid.coe_one, map_one, mul_one]; rfl
 #align localization.mk_algebra_map Localization.mk_algebraMap
 
-theorem mk_nat_cast (m : ℕ) : (mk m 1 : Localization M) = m := by
+theorem mk_natCast (m : ℕ) : (mk m 1 : Localization M) = m := by
   simpa using mk_algebraMap (R := R) (A := ℕ) _
-#align localization.mk_nat_cast Localization.mk_nat_cast
+#align localization.mk_nat_cast Localization.mk_natCast
 
 variable [IsLocalization M S]
 
@@ -1213,9 +1213,9 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d =
     _ = mk (d * a - b * c) (b * d) := by congr; ring
 #align localization.sub_mk Localization.sub_mk
 
-theorem mk_int_cast (m : ℤ) : (mk m 1 : Localization M) = m := by
+theorem mk_intCast (m : ℤ) : (mk m 1 : Localization M) = m := by
   simpa using mk_algebraMap (R := R) (A := ℤ) _
-#align localization.mk_int_cast Localization.mk_int_cast
+#align localization.mk_int_cast Localization.mk_intCast
 
 end Localization
 

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

@@ -1209,7 +1209,7 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d =
   calc
     mk a b - mk c d = mk a b + -mk c d := sub_eq_add_neg _ _
     _ = mk a b + mk (-c) d := by rw [neg_mk]
-    _ = mk (b * -c + d * a) (b * d) := (add_mk _ _ _ _)
+    _ = mk (b * -c + d * a) (b * d) := add_mk _ _ _ _
     _ = mk (d * a - b * c) (b * d) := by congr; ring
 #align localization.sub_mk Localization.sub_mk
 

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.

@@ -1186,7 +1186,7 @@ instance : CommRing (Localization M) :=
       Localization.induction_on x fun x => by simp only [smul_mk, zero_zsmul, mk_zero]
     zsmul_succ' := fun n x =>
       Localization.induction_on x fun x => by
-        simp [smul_mk, add_mk_self, -mk_eq_monoidOf_mk', add_comm (n : ℤ) 1, add_smul]
+        simp [smul_mk, add_mk_self, -mk_eq_monoidOf_mk', add_smul]
     zsmul_neg' := fun n x =>
       Localization.induction_on x fun x => by
         dsimp only

Classifies by adding issue number #10618 to porting notes claiming "simp can prove it".

@@ -718,7 +718,7 @@ theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T
   rfl
 #align is_localization.ring_equiv_of_ring_equiv_eq_map IsLocalization.ringEquivOfRingEquiv_eq_map
 
--- Porting note: removed `simp`, `simp` can prove it
+-- Porting note (#10618): removed `simp`, `simp` can prove it
 theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x) :
     ringEquivOfRingEquiv S Q j H ((algebraMap R S) x) = algebraMap P Q (j x) := by
   simp
@@ -750,12 +750,12 @@ noncomputable def algEquiv : S ≃ₐ[R] Q :=
 
 end
 
--- Porting note: removed `simp`, `simp` can prove it
+-- Porting note (#10618): removed `simp`, `simp` can prove it
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
   by simp
 #align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'
 
--- Porting note: removed `simp`, `simp` can prove it
+-- Porting note (#10618): removed `simp`, `simp` can prove it
 theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) = mk' S x y := by simp
 #align is_localization.alg_equiv_symm_mk' IsLocalization.algEquiv_symm_mk'
 
@@ -1121,12 +1121,12 @@ noncomputable def _root_.IsLocalization.unique (R Rₘ) [CommSemiring R] [CommSe
 
 end
 
--- Porting note: removed `simp`, `simp` can prove it
+-- Porting note (#10618): removed `simp`, `simp` can prove it
 nonrec theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) = mk' S x y :=
   algEquiv_mk' _ _
 #align localization.alg_equiv_mk' Localization.algEquiv_mk'
 
--- Porting note: removed `simp`, `simp` can prove it
+-- Porting note (#10618): removed `simp`, `simp` can prove it
 nonrec theorem algEquiv_symm_mk' (x : R) (y : M) :
     (algEquiv M S).symm (mk' S x y) = mk' (Localization M) x y :=
   algEquiv_symm_mk' _ _

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)

@@ -91,7 +91,6 @@ open BigOperators
 section CommSemiring
 
 variable {R : Type*} [CommSemiring R] (M : Submonoid R) (S : Type*) [CommSemiring S]
-
 variable [Algebra R S] {P : Type*} [CommSemiring P]
 
 /-- The typeclass `IsLocalization (M : Submonoid R) S` where `S` is an `R`-algebra
@@ -613,7 +612,6 @@ theorem lift_injective_iff :
 section Map
 
 variable {T : Submonoid P} {Q : Type*} [CommSemiring Q] (hy : M ≤ T.comap g)
-
 variable [Algebra P Q] [IsLocalization T Q]
 
 section
@@ -1156,7 +1154,6 @@ end CommSemiring
 section CommRing
 
 variable {R : Type*} [CommRing R] {M : Submonoid R} (S : Type*) [CommRing S]
-
 variable [Algebra R S] {P : Type*} [CommRing P]
 
 namespace Localization
@@ -1264,7 +1261,6 @@ theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDiv
 #align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zero
 
 variable {Q : Type*} [CommRing Q] {g : R →+* P} [Algebra P Q]
-
 variable (A : Type*) [CommRing A] [IsDomain A]
 
 /-- A `CommRing` `S` which is the localization of a ring `R` without zero divisors at a subset of
@@ -1337,9 +1333,7 @@ theorem Field.localization_map_bijective {K Kₘ : Type*} [Field K] [CommRing K
 section Algebra
 
 variable {S} {Rₘ Sₘ : Type*} [CommRing Rₘ] [CommRing Sₘ]
-
 variable [Algebra R Rₘ] [IsLocalization M Rₘ]
-
 variable [Algebra S Sₘ] [i : IsLocalization (Algebra.algebraMapSubmonoid S M) Sₘ]
 
 section
@@ -1367,7 +1361,6 @@ end
 section
 
 variable [Algebra Rₘ Sₘ] [Algebra R Sₘ] [IsScalarTower R Rₘ Sₘ] [IsScalarTower R S Sₘ]
-
 variable (S Rₘ Sₘ)
 
 theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R Sₘ y) := by

Classifies by adding issue number #10756 to porting notes claiming anything equivalent to:

• "added theorem"
• "added theorems"
• "new theorem"
• "new theorems"
• "added lemma"
• "new lemma"
• "new lemmas"

@@ -648,7 +648,7 @@ theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.
     (fun y => hy y.2) (k := toLocalizationMap T Q) ..
 #align is_localization.map_mk' IsLocalization.map_mk'
 
--- Porting note: new theorem
+-- Porting note (#10756): new theorem
 @[simp]
 theorem map_id_mk' {Q : Type*} [CommSemiring Q] [Algebra R Q] [IsLocalization M Q] (x) (y : M) :
     map Q (RingHom.id R) (le_refl M) (mk' S x y) = mk' Q x y :=

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -97,7 +97,7 @@ variable [Algebra R S] {P : Type*} [CommSemiring P]
 /-- The typeclass `IsLocalization (M : Submonoid R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
 @[mk_iff] class IsLocalization : Prop where
-  --Porting note: add ' to fields, and made new versions of these with either `S` or `M` explicit.
+  -- Porting note: add ' to fields, and made new versions of these with either `S` or `M` explicit.
   /-- Everything in the image of `algebraMap` is a unit -/
   map_units' : ∀ y : M, IsUnit (algebraMap R S y)
   /-- The `algebraMap` is surjective -/
@@ -632,7 +632,7 @@ noncomputable def map (g : R →+* P) (hy : M ≤ T.comap g) : S →+* Q :=
 
 end
 
---Porting note: added `simp` attribute, since it proves very similar lemmas marked `simp`
+-- Porting note: added `simp` attribute, since it proves very similar lemmas marked `simp`
 @[simp]
 theorem map_eq (x) : map Q g hy ((algebraMap R S) x) = algebraMap P Q (g x) :=
   lift_eq (fun y => map_units _ ⟨g y, hy y.2⟩) x
@@ -648,7 +648,7 @@ theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.
     (fun y => hy y.2) (k := toLocalizationMap T Q) ..
 #align is_localization.map_mk' IsLocalization.map_mk'
 
---Porting note: new theorem
+-- Porting note: new theorem
 @[simp]
 theorem map_id_mk' {Q : Type*} [CommSemiring Q] [Algebra R Q] [IsLocalization M Q] (x) (y : M) :
     map Q (RingHom.id R) (le_refl M) (mk' S x y) = mk' Q x y :=
@@ -720,7 +720,7 @@ theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T
   rfl
 #align is_localization.ring_equiv_of_ring_equiv_eq_map IsLocalization.ringEquivOfRingEquiv_eq_map
 
---Porting note: removed `simp`, `simp` can prove it
+-- Porting note: removed `simp`, `simp` can prove it
 theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x) :
     ringEquivOfRingEquiv S Q j H ((algebraMap R S) x) = algebraMap P Q (j x) := by
   simp
@@ -752,12 +752,12 @@ noncomputable def algEquiv : S ≃ₐ[R] Q :=
 
 end
 
---Porting note: removed `simp`, `simp` can prove it
+-- Porting note: removed `simp`, `simp` can prove it
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
   by simp
 #align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'
 
---Porting note: removed `simp`, `simp` can prove it
+-- Porting note: removed `simp`, `simp` can prove it
 theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) = mk' S x y := by simp
 #align is_localization.alg_equiv_symm_mk' IsLocalization.algEquiv_symm_mk'
 
@@ -1087,7 +1087,7 @@ theorem mk_eq_mk'_apply (x y) : mk x y = IsLocalization.mk' (Localization M) x y
   rw [mk_eq_monoidOf_mk'_apply, mk', toLocalizationMap_eq_monoidOf]
 #align localization.mk_eq_mk'_apply Localization.mk_eq_mk'_apply
 
---Porting note: removed `simp`. Left hand side can be simplified; not clear what normal form should
+-- Porting note: removed `simp`. Left hand side can be simplified; not clear what normal form should
 --be.
 theorem mk_eq_mk' : (mk : R → M → Localization M) = IsLocalization.mk' (Localization M) :=
   mk_eq_monoidOf_mk'
@@ -1123,12 +1123,12 @@ noncomputable def _root_.IsLocalization.unique (R Rₘ) [CommSemiring R] [CommSe
 
 end
 
---Porting note: removed `simp`, `simp` can prove it
+-- Porting note: removed `simp`, `simp` can prove it
 nonrec theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S (mk' (Localization M) x y) = mk' S x y :=
   algEquiv_mk' _ _
 #align localization.alg_equiv_mk' Localization.algEquiv_mk'
 
---Porting note: removed `simp`, `simp` can prove it
+-- Porting note: removed `simp`, `simp` can prove it
 nonrec theorem algEquiv_symm_mk' (x : R) (y : M) :
     (algEquiv M S).symm (mk' S x y) = mk' (Localization M) x y :=
   algEquiv_symm_mk' _ _

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>

@@ -7,6 +7,7 @@ import Mathlib.Algebra.Algebra.Tower
 import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
 import Mathlib.GroupTheory.MonoidLocalization
 import Mathlib.RingTheory.Ideal.Basic
+import Mathlib.GroupTheory.GroupAction.Ring
 
 #align_import ring_theory.localization.basic from "leanprover-community/mathlib"@"b69c9a770ecf37eb21f7b8cf4fa00de3b62694ec"
 

Co-authored-by: Xavier Xarles <56635243+XavierXarles@users.noreply.github.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -173,6 +173,10 @@ theorem toLocalizationMap_toMap_apply (x) : (toLocalizationMap M S).toMap x = al
   rfl
 #align is_localization.to_localization_map_to_map_apply IsLocalization.toLocalizationMap_toMap_apply
 
+theorem surj₂ : ∀ z w : S, ∃ z' w' : R, ∃ d : M,
+    (z * algebraMap R S d = algebraMap R S z') ∧ (w * algebraMap R S d = algebraMap R S w') :=
+  (toLocalizationMap M S).surj₂
+
 end
 
 variable (M) {S}
@@ -786,6 +790,17 @@ noncomputable def atUnits (H : M ≤ IsUnit.submonoid R) : R ≃ₐ[R] S := by
 
 end at_units
 
+section
+
+variable (M S) (Q : Type*) [CommSemiring Q] [Algebra P Q]
+
+/-- Injectivity of a map descends to the map induced on localizations. -/
+theorem map_injective_of_injective (h : Function.Injective g) [IsLocalization (M.map g) Q] :
+    Function.Injective (map Q g M.le_comap_map : S → Q) :=
+  (toLocalizationMap M S).map_injective_of_injective h (toLocalizationMap (M.map g) Q)
+
+end
+
 end IsLocalization
 
 section
@@ -1247,25 +1262,7 @@ theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDiv
   · exact IsLocalization.injective S hM
 #align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zero
 
-variable (S M) (Q : Type*) [CommRing Q] {g : R →+* P} [Algebra P Q]
-
-/-- Injectivity of a map descends to the map induced on localizations. -/
-theorem map_injective_of_injective (hg : Function.Injective g)
-    [i : IsLocalization (M.map g : Submonoid P) Q] :
-    Function.Injective (map Q g (Submonoid.le_comap_map M) : S → Q) := by
-  rw [injective_iff_map_eq_zero]
-  intro z hz
-  obtain ⟨a, b, rfl⟩ := mk'_surjective M z
-  rw [map_mk', mk'_eq_zero_iff] at hz
-  obtain ⟨⟨m', hm'⟩, hm⟩ := hz
-  rw [Submonoid.mem_map] at hm'
-  obtain ⟨n, hn, hnm⟩ := hm'
-  rw [Subtype.coe_mk, ← hnm, ← map_mul, ← map_zero g] at hm
-  rw [mk'_eq_zero_iff]
-  exact ⟨⟨n, hn⟩, hg hm⟩
-#align is_localization.map_injective_of_injective IsLocalization.map_injective_of_injective
-
-variable {S Q M}
+variable {Q : Type*} [CommRing Q] {g : R →+* P} [Algebra P Q]
 
 variable (A : Type*) [CommRing A] [IsDomain A]
 
@@ -1434,7 +1431,8 @@ variable (Rₘ Sₘ)
 /-- Injectivity of the underlying `algebraMap` descends to the algebra induced by localization. -/
 theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)) :
     Function.Injective (@algebraMap Rₘ Sₘ _ _ (localizationAlgebra M S)) :=
-  IsLocalization.map_injective_of_injective (M := M) _ hRS (i := i)
+  have : IsLocalization (M.map (algebraMap R S)) Sₘ := i
+  IsLocalization.map_injective_of_injective _ _ _ hRS
 #align localization_algebra_injective localizationAlgebra_injective
 
 end Algebra

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>

@@ -537,12 +537,12 @@ theorem lift_eq_iff {x y : R × M} :
 
 @[simp]
 theorem lift_comp : (lift hg).comp (algebraMap R S) = g :=
-  RingHom.ext <| (FunLike.ext_iff (F := MonoidHom _ _)).1 <| (toLocalizationMap M S).lift_comp _
+  RingHom.ext <| (DFunLike.ext_iff (F := MonoidHom _ _)).1 <| (toLocalizationMap M S).lift_comp _
 #align is_localization.lift_comp IsLocalization.lift_comp
 
 @[simp]
 theorem lift_of_comp (j : S →+* P) : lift (isUnit_comp M j) = j :=
-  RingHom.ext <| (FunLike.ext_iff (F := MonoidHom _ _)).1 <|
+  RingHom.ext <| (DFunLike.ext_iff (F := MonoidHom _ _)).1 <|
     (toLocalizationMap M S).lift_of_comp j.toMonoidHom
 #align is_localization.lift_of_comp IsLocalization.lift_of_comp
 
@@ -551,7 +551,7 @@ variable (M)
 /-- See note [partially-applied ext lemmas] -/
 theorem monoidHom_ext ⦃j k : S →* P⦄
     (h : j.comp (algebraMap R S : R →* S) = k.comp (algebraMap R S)) : j = k :=
-  Submonoid.LocalizationMap.epic_of_localizationMap (toLocalizationMap M S) <| FunLike.congr_fun h
+  Submonoid.LocalizationMap.epic_of_localizationMap (toLocalizationMap M S) <| DFunLike.congr_fun h
 #align is_localization.monoid_hom_ext IsLocalization.monoidHom_ext
 
 /-- See note [partially-applied ext lemmas] -/
@@ -585,7 +585,7 @@ variable {M}
 
 theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) : lift hg = j :=
   RingHom.ext <|
-    (FunLike.ext_iff (F := MonoidHom _ _)).1 <|
+    (DFunLike.ext_iff (F := MonoidHom _ _)).1 <|
       Submonoid.LocalizationMap.lift_unique (toLocalizationMap M S) (g := g.toMonoidHom) hg
         (j := j.toMonoidHom) hj
 #align is_localization.lift_unique IsLocalization.lift_unique
@@ -1418,7 +1418,7 @@ theorem IsLocalization.algebraMap_apply_eq_map_map_submonoid (x) :
     algebraMap Rₘ Sₘ x =
       map Sₘ (algebraMap R S)
         (show _ ≤ (Algebra.algebraMapSubmonoid S M).comap _ from M.le_comap_map) x :=
-  FunLike.congr_fun (IsLocalization.algebraMap_eq_map_map_submonoid _ _ _ _) x
+  DFunLike.congr_fun (IsLocalization.algebraMap_eq_map_map_submonoid _ _ _ _) x
 #align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoid
 
 theorem IsLocalization.lift_algebraMap_eq_algebraMap :

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>

@@ -4,11 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
 -/
 import Mathlib.Algebra.Algebra.Tower
-import Mathlib.Algebra.Ring.Equiv
+import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
 import Mathlib.GroupTheory.MonoidLocalization
 import Mathlib.RingTheory.Ideal.Basic
-import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
-import Mathlib.Tactic.Ring
 
 #align_import ring_theory.localization.basic from "leanprover-community/mathlib"@"b69c9a770ecf37eb21f7b8cf4fa00de3b62694ec"
 
@@ -97,7 +95,7 @@ variable [Algebra R S] {P : Type*} [CommSemiring P]
 
 /-- The typeclass `IsLocalization (M : Submonoid R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
-class IsLocalization : Prop where
+@[mk_iff] class IsLocalization : Prop where
   --Porting note: add ' to fields, and made new versions of these with either `S` or `M` explicit.
   /-- Everything in the image of `algebraMap` is a unit -/
   map_units' : ∀ y : M, IsUnit (algebraMap R S y)

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.

@@ -383,6 +383,9 @@ theorem mk'_eq_of_eq' {a₁ b₁ : R} {a₂ b₂ : M} (H : b₁ * ↑a₂ = a₁
   (toLocalizationMap M S).mk'_eq_of_eq' H
 #align is_localization.mk'_eq_of_eq' IsLocalization.mk'_eq_of_eq'
 
+theorem mk'_cancel (a : R) (b c : M) :
+    mk' S (a * c) (b * c) = mk' S a b := (toLocalizationMap M S).mk'_cancel _ _ _
+
 variable (S)
 
 @[simp]

@@ -206,6 +206,9 @@ theorem sec_spec' (z : S) :
 
 variable {M}
 
+/-- If `M` contains `0` then the localization at `M` is trivial. -/
+theorem subsingleton (h : 0 ∈ M) : Subsingleton S := (toLocalizationMap M S).subsingleton h
+
 theorem map_right_cancel {x y} {c : M} (h : algebraMap R S (c * x) = algebraMap R S (c * y)) :
     algebraMap R S x = algebraMap R S y :=
   (toLocalizationMap M S).map_right_cancel h

@@ -811,8 +811,8 @@ theorem isLocalization_iff_of_algEquiv [Algebra R P] (h : S ≃ₐ[R] P) :
 #align is_localization.is_localization_iff_of_alg_equiv IsLocalization.isLocalization_iff_of_algEquiv
 
 theorem isLocalization_iff_of_ringEquiv (h : S ≃+* P) :
-    IsLocalization M S ↔ have := (h.toRingHom.comp <| algebraMap R S).toAlgebra;
-      IsLocalization M P :=
+    IsLocalization M S ↔
+      haveI := (h.toRingHom.comp <| algebraMap R S).toAlgebra; IsLocalization M P :=
   letI := (h.toRingHom.comp <| algebraMap R S).toAlgebra
   isLocalization_iff_of_algEquiv M { h with commutes' := fun _ => rfl }
 #align is_localization.is_localization_iff_of_ring_equiv IsLocalization.isLocalization_iff_of_ringEquiv
@@ -820,8 +820,8 @@ theorem isLocalization_iff_of_ringEquiv (h : S ≃+* P) :
 variable (S)
 
 theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
-    have := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra;
-      IsLocalization (M.map h.toMonoidHom) S := by
+    haveI := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra
+    IsLocalization (M.map h.toMonoidHom) S := by
   letI : Algebra P S := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra
   constructor
   · rintro ⟨_, ⟨y, hy, rfl⟩⟩
@@ -843,7 +843,8 @@ theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
 #align is_localization.is_localization_of_base_ring_equiv IsLocalization.isLocalization_of_base_ringEquiv
 
 theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
-    IsLocalization M S ↔ haveI := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra;
+    IsLocalization M S ↔
+      haveI := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra
       IsLocalization (M.map h.toMonoidHom) S := by
   letI : Algebra P S := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra
   refine' ⟨fun _ => isLocalization_of_base_ringEquiv M S h, _⟩

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

@@ -7,7 +7,7 @@ import Mathlib.Algebra.Algebra.Tower
 import Mathlib.Algebra.Ring.Equiv
 import Mathlib.GroupTheory.MonoidLocalization
 import Mathlib.RingTheory.Ideal.Basic
-import Mathlib.RingTheory.NonZeroDivisors
+import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
 import Mathlib.Tactic.Ring
 
 #align_import ring_theory.localization.basic from "leanprover-community/mathlib"@"b69c9a770ecf37eb21f7b8cf4fa00de3b62694ec"

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

@@ -456,7 +456,7 @@ end
 `g : R →+* P` such that `g(M) ⊆ Units P`, `f x = f y → g x = g y` for all `x y : R`. -/
 theorem eq_of_eq {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) {x y}
     (h : (algebraMap R S) x = (algebraMap R S) y) : g x = g y :=
-  @Submonoid.LocalizationMap.eq_of_eq _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom hg _ _ h
+  Submonoid.LocalizationMap.eq_of_eq (toLocalizationMap M S) (g := g.toMonoidHom) hg h
 #align is_localization.eq_of_eq IsLocalization.eq_of_eq
 
 theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
@@ -582,8 +582,8 @@ variable {M}
 theorem lift_unique {j : S →+* P} (hj : ∀ x, j ((algebraMap R S) x) = g x) : lift hg = j :=
   RingHom.ext <|
     (FunLike.ext_iff (F := MonoidHom _ _)).1 <|
-      @Submonoid.LocalizationMap.lift_unique _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom hg
-        j.toMonoidHom hj
+      Submonoid.LocalizationMap.lift_unique (toLocalizationMap M S) (g := g.toMonoidHom) hg
+        (j := j.toMonoidHom) hj
 #align is_localization.lift_unique IsLocalization.lift_unique
 
 @[simp]
@@ -618,7 +618,7 @@ such that `g(M) ⊆ T`.
 We send `z : S` to `algebraMap P Q (g x) * (algebraMap P Q (g y))⁻¹`, where
 `(x, y) : R × M` are such that `z = f x * (f y)⁻¹`. -/
 noncomputable def map (g : R →+* P) (hy : M ≤ T.comap g) : S →+* Q :=
-  @lift R _ M _ _ _ _ _ _ ((algebraMap P Q).comp g) fun y => map_units _ ⟨g y, hy y.2⟩
+  lift (M := M) (g := (algebraMap P Q).comp g) fun y => map_units _ ⟨g y, hy y.2⟩
 #align is_localization.map IsLocalization.map
 
 end
@@ -635,15 +635,15 @@ theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g
 #align is_localization.map_comp IsLocalization.map_comp
 
 theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.2⟩ :=
-  @Submonoid.LocalizationMap.map_mk' _ _ _ _ _ _ _ (toLocalizationMap M S) g.toMonoidHom _
-    (fun y => hy y.2) _ _ (toLocalizationMap T Q) _ _
+  Submonoid.LocalizationMap.map_mk' (toLocalizationMap M S) (g := g.toMonoidHom)
+    (fun y => hy y.2) (k := toLocalizationMap T Q) ..
 #align is_localization.map_mk' IsLocalization.map_mk'
 
 --Porting note: new theorem
 @[simp]
 theorem map_id_mk' {Q : Type*} [CommSemiring Q] [Algebra R Q] [IsLocalization M Q] (x) (y : M) :
     map Q (RingHom.id R) (le_refl M) (mk' S x y) = mk' Q x y :=
-  map_mk' _ _ _
+  map_mk' ..
 
 @[simp]
 theorem map_id (z : S) (h : M ≤ M.comap (RingHom.id R) := le_refl M) :
@@ -662,8 +662,8 @@ theorem map_comp_map {A : Type*} [CommSemiring A] {U : Submonoid A} {W} [CommSem
     [Algebra A W] [IsLocalization U W] {l : P →+* A} (hl : T ≤ U.comap l) :
     (map W l hl).comp (map Q g hy : S →+* _) = map W (l.comp g) fun _ hx => hl (hy hx) :=
   RingHom.ext fun x =>
-    @Submonoid.LocalizationMap.map_map _ _ _ _ _ P _ (toLocalizationMap M S) g _ (fun y => hy y.2)
-      _ _ _ _ _ _ _ _ (toLocalizationMap U W) l (fun w => hl w.2) x
+    Submonoid.LocalizationMap.map_map (P := P) (toLocalizationMap M S) (fun y => hy y.2)
+      (toLocalizationMap U W) (fun w => hl w.2) x
 #align is_localization.map_comp_map IsLocalization.map_comp_map
 
 /-- If `CommSemiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
@@ -811,7 +811,8 @@ theorem isLocalization_iff_of_algEquiv [Algebra R P] (h : S ≃ₐ[R] P) :
 #align is_localization.is_localization_iff_of_alg_equiv IsLocalization.isLocalization_iff_of_algEquiv
 
 theorem isLocalization_iff_of_ringEquiv (h : S ≃+* P) :
-    IsLocalization M S ↔ @IsLocalization _ _ M P _ (h.toRingHom.comp <| algebraMap R S).toAlgebra :=
+    IsLocalization M S ↔ have := (h.toRingHom.comp <| algebraMap R S).toAlgebra;
+      IsLocalization M P :=
   letI := (h.toRingHom.comp <| algebraMap R S).toAlgebra
   isLocalization_iff_of_algEquiv M { h with commutes' := fun _ => rfl }
 #align is_localization.is_localization_iff_of_ring_equiv IsLocalization.isLocalization_iff_of_ringEquiv
@@ -819,8 +820,8 @@ theorem isLocalization_iff_of_ringEquiv (h : S ≃+* P) :
 variable (S)
 
 theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
-    @IsLocalization _ _ (M.map h.toMonoidHom) S _
-      ((algebraMap R S).comp h.symm.toRingHom).toAlgebra := by
+    have := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra;
+      IsLocalization (M.map h.toMonoidHom) S := by
   letI : Algebra P S := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra
   constructor
   · rintro ⟨_, ⟨y, hy, rfl⟩⟩
@@ -842,9 +843,8 @@ theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
 #align is_localization.is_localization_of_base_ring_equiv IsLocalization.isLocalization_of_base_ringEquiv
 
 theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
-    IsLocalization M S ↔
-      @IsLocalization _ _ (M.map h.toMonoidHom) S _
-        ((algebraMap R S).comp h.symm.toRingHom).toAlgebra := by
+    IsLocalization M S ↔ haveI := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra;
+      IsLocalization (M.map h.toMonoidHom) S := by
   letI : Algebra P S := ((algebraMap R S).comp h.symm.toRingHom).toAlgebra
   refine' ⟨fun _ => isLocalization_of_base_ringEquiv M S h, _⟩
   intro H
@@ -1078,7 +1078,7 @@ theorem mk_algebraMap {A : Type*} [CommSemiring A] [Algebra A R] (m : A) :
 #align localization.mk_algebra_map Localization.mk_algebraMap
 
 theorem mk_nat_cast (m : ℕ) : (mk m 1 : Localization M) = m := by
-  simpa using @mk_algebraMap R _ M ℕ _ _ m
+  simpa using mk_algebraMap (R := R) (A := ℕ) _
 #align localization.mk_nat_cast Localization.mk_nat_cast
 
 variable [IsLocalization M S]
@@ -1196,7 +1196,7 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d =
 #align localization.sub_mk Localization.sub_mk
 
 theorem mk_int_cast (m : ℤ) : (mk m 1 : Localization M) = m := by
-  simpa using @mk_algebraMap R _ M ℤ _ _ m
+  simpa using mk_algebraMap (R := R) (A := ℤ) _
 #align localization.mk_int_cast Localization.mk_int_cast
 
 end Localization
@@ -1247,8 +1247,7 @@ variable (S M) (Q : Type*) [CommRing Q] {g : R →+* P} [Algebra P Q]
 /-- Injectivity of a map descends to the map induced on localizations. -/
 theorem map_injective_of_injective (hg : Function.Injective g)
     [i : IsLocalization (M.map g : Submonoid P) Q] :
-    --Porting note: Why does `i` need to be given explicitly?
-    Function.Injective (@map _ _ _ _ _ _ _ _ _ _ Q _ _ i g (Submonoid.le_comap_map M) : S → Q) := by
+    Function.Injective (map Q g (Submonoid.le_comap_map M) : S → Q) := by
   rw [injective_iff_map_eq_zero]
   intro z hz
   obtain ⟨a, b, rfl⟩ := mk'_surjective M z
@@ -1418,8 +1417,7 @@ theorem IsLocalization.algebraMap_apply_eq_map_map_submonoid (x) :
 #align is_localization.algebra_map_apply_eq_map_map_submonoid IsLocalization.algebraMap_apply_eq_map_map_submonoid
 
 theorem IsLocalization.lift_algebraMap_eq_algebraMap :
-    @IsLocalization.lift R _ M Rₘ _ _ Sₘ _ _ (algebraMap R Sₘ)
-        (IsLocalization.map_units_map_submonoid S Sₘ) =
+    IsLocalization.lift (M := M) (IsLocalization.map_units_map_submonoid S Sₘ) =
       algebraMap Rₘ Sₘ :=
   IsLocalization.lift_unique _ fun _ => (IsScalarTower.algebraMap_apply _ _ _ _).symm
 #align is_localization.lift_algebra_map_eq_algebra_map IsLocalization.lift_algebraMap_eq_algebraMap
@@ -1431,9 +1429,7 @@ variable (Rₘ Sₘ)
 /-- Injectivity of the underlying `algebraMap` descends to the algebra induced by localization. -/
 theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)) :
     Function.Injective (@algebraMap Rₘ Sₘ _ _ (localizationAlgebra M S)) :=
-  --Porting note: I don't understand why `i` needs to be explicit or why writing `(i := i)`
-  --doesn't work.
-  @IsLocalization.map_injective_of_injective _ _ M Rₘ _ _ _ _ _ Sₘ _ _ _ hRS i
+  IsLocalization.map_injective_of_injective (M := M) _ hRS (i := i)
 #align localization_algebra_injective localizationAlgebra_injective
 
 end Algebra

@@ -979,7 +979,7 @@ def mkAddMonoidHom (b : M) : R →+ Localization M where
 
 theorem mk_sum {ι : Type*} (f : ι → R) (s : Finset ι) (b : M) :
     mk (∑ i in s, f i) b = ∑ i in s, mk (f i) b :=
-  (mkAddMonoidHom b).map_sum f s
+  map_sum (mkAddMonoidHom b) f s
 #align localization.mk_sum Localization.mk_sum
 
 theorem mk_list_sum (l : List R) (b : M) : mk l.sum b = (l.map fun a => mk a b).sum :=

@@ -436,6 +436,12 @@ theorem smul_mk' (x y : R) (m : M) : x • mk' S y m = mk' S (x * y) m := by
     (m : R) • mk' S r m = algebraMap R S r := by
   rw [smul_mk', mk'_mul_cancel_left]
 
+@[simps]
+instance invertible_mk'_one (s : M) : Invertible (IsLocalization.mk' S (1 : R) s) where
+  invOf := algebraMap R S s
+  invOf_mul_self := by simp
+  mul_invOf_self := by simp
+
 section
 
 variable (M)
@@ -748,6 +754,34 @@ theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) =
 
 end AlgEquiv
 
+section at_units
+
+lemma at_units {R : Type*} [CommSemiring R] (S : Submonoid R)
+    (hS : S ≤ IsUnit.submonoid R) : IsLocalization S R where
+  map_units' y := hS y.prop
+  surj' := fun s ↦ ⟨⟨s, 1⟩, by simp⟩
+  exists_of_eq := fun {x y} (e : x = y) ↦ ⟨1, e ▸ rfl⟩
+
+variable (R M)
+
+/-- The localization at a module of units is isomorphic to the ring. -/
+noncomputable def atUnits (H : M ≤ IsUnit.submonoid R) : R ≃ₐ[R] S := by
+  refine' AlgEquiv.ofBijective (Algebra.ofId R S) ⟨_, _⟩
+  · intro x y hxy
+    obtain ⟨c, eq⟩ := (IsLocalization.eq_iff_exists M S).mp hxy
+    obtain ⟨u, hu⟩ := H c.prop
+    rwa [← hu, Units.mul_right_inj] at eq
+  · intro y
+    obtain ⟨⟨x, s⟩, eq⟩ := IsLocalization.surj M y
+    obtain ⟨u, hu⟩ := H s.prop
+    use x * u.inv
+    dsimp [Algebra.ofId, RingHom.toFun_eq_coe, AlgHom.coe_mks]
+    rw [RingHom.map_mul, ← eq, ← hu, mul_assoc, ← RingHom.map_mul]
+    simp
+#align is_localization.at_units IsLocalization.atUnits
+
+end at_units
+
 end IsLocalization
 
 section

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>

@@ -20,7 +20,8 @@ isomorphism; that is, a commutative ring `S` is the localization of `R` at `M` i
 ring homomorphism `f : R →+* S` satisfying 3 properties:
 1. For all `y ∈ M`, `f y` is a unit;
 2. For all `z : S`, there exists `(x, y) : R × M` such that `z * f y = f x`;
-3. For all `x, y : R`, `f x = f y` iff there exists `c ∈ M` such that `x * c = y * c`.
+3. For all `x, y : R` such that `f x = f y`, there exists `c ∈ M` such that `x * c = y * c`.
+   (The converse is a consequence of 1.)
 
 In the following, let `R, P` be commutative rings, `S, Q` be `R`- and `P`-algebras
 and `M, T` be submonoids of `R` and `P` respectively, e.g.:
@@ -100,10 +101,11 @@ class IsLocalization : Prop where
   --Porting note: add ' to fields, and made new versions of these with either `S` or `M` explicit.
   /-- Everything in the image of `algebraMap` is a unit -/
   map_units' : ∀ y : M, IsUnit (algebraMap R S y)
-  /-- the `algebraMap` is surjective -/
+  /-- The `algebraMap` is surjective -/
   surj' : ∀ z : S, ∃ x : R × M, z * algebraMap R S x.2 = algebraMap R S x.1
-  /-- The kernel of `algebraMap` is the annihilator of `M` -/
-  eq_iff_exists' : ∀ {x y}, algebraMap R S x = algebraMap R S y ↔ ∃ c : M, ↑c * x = ↑c * y
+  /-- The kernel of `algebraMap` is contained in the annihilator of `M`;
+      it is then equal to the annihilator by `map_units'` -/
+  exists_of_eq : ∀ {x y}, algebraMap R S x = algebraMap R S y → ∃ c : M, ↑c * x = ↑c * y
 #align is_localization IsLocalization
 
 variable {M}
@@ -126,25 +128,24 @@ theorem surj : ∀ z : S, ∃ x : R × M, z * algebraMap R S x.2 = algebraMap R
   IsLocalization.surj'
 
 variable (S)
-@[inherit_doc IsLocalization.eq_iff_exists']
+@[inherit_doc IsLocalization.exists_of_eq]
 theorem eq_iff_exists {x y} : algebraMap R S x = algebraMap R S y ↔ ∃ c : M, ↑c * x = ↑c * y :=
-  IsLocalization.eq_iff_exists'
+  Iff.intro IsLocalization.exists_of_eq fun ⟨c, h⟩ ↦ by
+    apply_fun algebraMap R S at h
+    rw [map_mul, map_mul] at h
+    exact (IsLocalization.map_units S c).mul_right_inj.mp h
 
 variable {S}
 theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (algebraMap R S r)) :
-    IsLocalization N S :=
-  { map_units' := fun r => h₂ r r.2
-    surj' := fun s => by
-      obtain ⟨⟨x, y, hy⟩, H⟩ := IsLocalization.surj M s
-      exact ⟨⟨x, y, h₁ hy⟩, H⟩
-    eq_iff_exists' := fun {x y} => by
-      constructor
-      · rw [IsLocalization.eq_iff_exists M]
-        rintro ⟨c, hc⟩
-        exact ⟨⟨c, h₁ c.2⟩, hc⟩
-      · rintro ⟨c, h⟩
-        simpa only [map_mul, (h₂ c c.2).mul_right_inj] using
-          congr_arg (algebraMap R S) h }
+    IsLocalization N S where
+  map_units' r := h₂ r r.2
+  surj' s :=
+    have ⟨⟨x, y, hy⟩, H⟩ := IsLocalization.surj M s
+    ⟨⟨x, y, h₁ hy⟩, H⟩
+  exists_of_eq {x y} := by
+    rw [IsLocalization.eq_iff_exists M]
+    rintro ⟨c, hc⟩
+    exact ⟨⟨c, h₁ c.2⟩, hc⟩
 #align is_localization.of_le IsLocalization.of_le
 
 variable (S)
@@ -152,12 +153,12 @@ variable (S)
 /-- `IsLocalization.toLocalizationWithZeroMap M S` shows `S` is the monoid localization of
 `R` at `M`. -/
 @[simps]
-def toLocalizationWithZeroMap : Submonoid.LocalizationWithZeroMap M S :=
-  { algebraMap R S with
-    toFun := algebraMap R S
-    map_units' := IsLocalization.map_units _
-    surj' := IsLocalization.surj _
-    eq_iff_exists' := fun _ _ => IsLocalization.eq_iff_exists _ _ }
+def toLocalizationWithZeroMap : Submonoid.LocalizationWithZeroMap M S where
+  __ := algebraMap R S
+  toFun := algebraMap R S
+  map_units' := IsLocalization.map_units _
+  surj' := IsLocalization.surj _
+  exists_of_eq _ _ := IsLocalization.exists_of_eq
 #align is_localization.to_localization_with_zero_map IsLocalization.toLocalizationWithZeroMap
 
 /-- `IsLocalization.toLocalizationMap M S` shows `S` is the monoid localization of `R` at `M`. -/
@@ -767,7 +768,7 @@ theorem isLocalization_of_algEquiv [Algebra R P] [IsLocalization M S] (h : S ≃
   · intro x y
     rw [← h.symm.toEquiv.injective.eq_iff, ← IsLocalization.eq_iff_exists M S, ← h.symm.commutes, ←
       h.symm.commutes]
-    rfl
+    exact id
 #align is_localization.is_localization_of_alg_equiv IsLocalization.isLocalization_of_algEquiv
 
 theorem isLocalization_iff_of_algEquiv [Algebra R P] (h : S ≃ₐ[R] P) :
@@ -801,10 +802,9 @@ theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
     rw [RingHom.algebraMap_toAlgebra, RingHom.comp_apply, RingHom.comp_apply,
       IsLocalization.eq_iff_exists M S]
     simp_rw [← h.toEquiv.apply_eq_iff_eq]
-    change (∃ c : M, h (c * h.symm x) = h (c * h.symm y)) ↔ _
+    change (∃ c : M, h (c * h.symm x) = h (c * h.symm y)) → _
     simp only [RingEquiv.apply_symm_apply, RingEquiv.map_mul]
-    exact
-      ⟨fun ⟨c, e⟩ => ⟨⟨_, _, c.prop, rfl⟩, e⟩, fun ⟨⟨_, c, h, e₁⟩, e₂⟩ => ⟨⟨_, h⟩, e₁.symm ▸ e₂⟩⟩
+    exact fun ⟨c, e⟩ ↦ ⟨⟨_, _, c.prop, rfl⟩, e⟩
 #align is_localization.is_localization_of_base_ring_equiv IsLocalization.isLocalization_of_base_ringEquiv
 
 theorem isLocalization_iff_of_base_ringEquiv (h : R ≃+* P) :
@@ -1011,7 +1011,7 @@ instance algebra {S : Type*} [CommSemiring S] [Algebra S R] : Algebra S (Localiz
 instance isLocalization : IsLocalization M (Localization M) where
   map_units' := (Localization.monoidOf M).map_units
   surj' := (Localization.monoidOf M).surj
-  eq_iff_exists' := (Localization.monoidOf M).eq_iff_exists
+  exists_of_eq := (Localization.monoidOf M).eq_iff_exists.mp
 
 end
 

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -459,7 +459,7 @@ theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
       (by
         rw [mul_comm (_ + _), mul_add, mul_mk'_eq_mk'_of_mul, mk'_add_eq_iff_add_mul_eq_mul,
           mul_comm (_ * _), ← mul_assoc, add_comm, ← map_mul, mul_mk'_eq_mk'_of_mul,
-          add_comm _ (mk' _ _ _), mk'_add_eq_iff_add_mul_eq_mul]
+          mk'_add_eq_iff_add_mul_eq_mul]
         simp only [map_add, Submonoid.coe_mul, map_mul]
         ring)
 #align is_localization.mk'_add IsLocalization.mk'_add
@@ -1339,7 +1339,7 @@ theorem IsLocalization.map_units_map_submonoid (y : M) : IsUnit (algebraMap R S
   exact IsLocalization.map_units Sₘ ⟨algebraMap R S y, Algebra.mem_algebraMapSubmonoid_of_mem y⟩
 #align is_localization.map_units_map_submonoid IsLocalization.map_units_map_submonoid
 
-@[simp]
+-- can't be simp, as `S` only appears on the RHS
 theorem IsLocalization.algebraMap_mk' (x : R) (y : M) :
     algebraMap Rₘ Sₘ (IsLocalization.mk' Rₘ x y) =
       IsLocalization.mk' Sₘ (algebraMap R S x)

Fixed AlgebraicGeometry/AffineSchemes.lean, AlgebraicGeometry/Morphisms/QuasiSeparated.lean and AlgebraicGeometry/Morphisms/RingHomProperties.lean.

Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -1086,6 +1086,14 @@ theorem algEquiv_symm_mk (x : R) (y : M) : (algEquiv M S).symm (mk' S x y) = mk
   rw [mk_eq_mk', algEquiv_symm_mk']
 #align localization.alg_equiv_symm_mk Localization.algEquiv_symm_mk
 
+lemma coe_algEquiv :
+    (Localization.algEquiv M S : Localization M →+* S) =
+    IsLocalization.map (M := M) (T := M) _ (RingHom.id R) le_rfl := rfl
+
+lemma coe_algEquiv_symm :
+    ((Localization.algEquiv M S).symm : S →+* Localization M) =
+    IsLocalization.map (M := M) (T := M) _ (RingHom.id R) le_rfl := rfl
+
 end Localization
 
 end CommSemiring

Purely cosmetic PR

@@ -424,7 +424,7 @@ theorem mk'_mul_mk'_eq_one' (x : R) (y : M) (h : x ∈ M) : mk' S x y * mk' S (y
   mk'_mul_mk'_eq_one ⟨x, h⟩ _
 #align is_localization.mk'_mul_mk'_eq_one' IsLocalization.mk'_mul_mk'_eq_one'
 
-theorem smul_mk' (x y : R) (m : M) : x • mk' S y m = mk' S (x * y) m  := by
+theorem smul_mk' (x y : R) (m : M) : x • mk' S y m = mk' S (x * y) m := by
   nth_rw 2 [← one_mul m]
   rw [mk'_mul, mk'_one, Algebra.smul_def]
 

@@ -94,7 +94,7 @@ variable {R : Type*} [CommSemiring R] (M : Submonoid R) (S : Type*) [CommSemirin
 
 variable [Algebra R S] {P : Type*} [CommSemiring P]
 
-/-- The typeclass `IsLocalization (M : Submodule R) S` where `S` is an `R`-algebra
+/-- The typeclass `IsLocalization (M : Submonoid R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
 class IsLocalization : Prop where
   --Porting note: add ' to fields, and made new versions of these with either `S` or `M` explicit.

@@ -25,8 +25,8 @@ ring homomorphism `f : R →+* S` satisfying 3 properties:
 In the following, let `R, P` be commutative rings, `S, Q` be `R`- and `P`-algebras
 and `M, T` be submonoids of `R` and `P` respectively, e.g.:
 ```
-variables (R S P Q : Type*) [CommRing R] [CommRing S] [CommRing P] [CommRing Q]
-variables [Algebra R S] [Algebra P Q] (M : Submonoid R) (T : Submonoid P)
+variable (R S P Q : Type*) [CommRing R] [CommRing S] [CommRing P] [CommRing Q]
+variable [Algebra R S] [Algebra P Q] (M : Submonoid R) (T : Submonoid P)
 ```
 
 ## Main definitions
@@ -137,7 +137,7 @@ theorem of_le (N : Submonoid R) (h₁ : M ≤ N) (h₂ : ∀ r ∈ N, IsUnit (al
     surj' := fun s => by
       obtain ⟨⟨x, y, hy⟩, H⟩ := IsLocalization.surj M s
       exact ⟨⟨x, y, h₁ hy⟩, H⟩
-    eq_iff_exists' := @fun x y => by
+    eq_iff_exists' := fun {x y} => by
       constructor
       · rw [IsLocalization.eq_iff_exists M]
         rintro ⟨c, hc⟩
@@ -486,8 +486,7 @@ theorem lift_spec_mul_add {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) (z w w'
 `S` to `P` sending `z : S` to `g x * (g y)⁻¹`, where `(x, y) : R × M` are such that
 `z = f x * (f y)⁻¹`. -/
 noncomputable def lift {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) : S →+* P :=
-  {
-    @Submonoid.LocalizationWithZeroMap.lift _ _ _ _ _ _ _ (toLocalizationWithZeroMap M S)
+  { Submonoid.LocalizationWithZeroMap.lift (toLocalizationWithZeroMap M S)
       g.toMonoidWithZeroHom hg with
     map_add' := by
       intro x y
@@ -496,7 +495,7 @@ noncomputable def lift {g : R →+* P} (hg : ∀ y : M, IsUnit (g y)) : S →+*
       simp_rw [← mul_assoc]
       show g _ * g _ * g _ + g _ * g _ * g _ = g _ * g _ * g _
       simp_rw [← map_mul g, ← map_add g]
-      apply @eq_of_eq _ _ _ S _ _ _ _ _ g hg
+      apply eq_of_eq (S := S) hg
       simp only [sec_spec', toLocalizationMap_sec, map_add, map_mul]
       ring }
 #align is_localization.lift IsLocalization.lift
@@ -686,8 +685,7 @@ noncomputable def ringEquivOfRingEquiv (h : R ≃+* P) (H : M.map h.toMonoidHom
     congr
     ext
     apply h.symm_apply_apply
-  {
-    map Q (h : R →+* P) (M.le_comap_of_map_le (le_of_eq H)) with
+  { map Q (h : R →+* P) (M.le_comap_of_map_le (le_of_eq H)) with
     toFun := map Q (h : R →+* P) (M.le_comap_of_map_le (le_of_eq H))
     invFun := map S (h.symm : P →+* R) (T.le_comap_of_map_le (le_of_eq H'))
     left_inv := fun x => by
@@ -869,7 +867,7 @@ Should not be confused with `AddLocalization.add`, which is defined as
 -/
 protected irreducible_def add (z w : Localization M) : Localization M :=
   Localization.liftOn₂ z w (fun a b c d => mk ((b : R) * c + d * a) (b * d))
-    @fun a a' b b' c c' d d' h1 h2 =>
+    fun {a a' b b' c c' d d'} h1 h2 =>
     mk_eq_mk_iff.2
       (by
         rw [r_eq_r'] at h1 h2 ⊢
@@ -939,8 +937,7 @@ instance : CommSemiring (Localization M) :=
 /-- For any given denominator `b : M`, the map `a ↦ a / b` is an `AddMonoidHom` from `R` to
   `Localization M`-/
 @[simps]
-def mkAddMonoidHom (b : M) : R →+ Localization M
-    where
+def mkAddMonoidHom (b : M) : R →+ Localization M where
   toFun a := mk a b
   map_zero' := mk_zero _
   map_add' _ _ := (add_mk_self _ _ _).symm
@@ -960,8 +957,7 @@ theorem mk_multiset_sum (l : Multiset R) (b : M) : mk l.sum b = (l.map fun a =>
 #align localization.mk_multiset_sum Localization.mk_multiset_sum
 
 instance {S : Type*} [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] :
-    DistribMulAction S (Localization M)
-    where
+    DistribMulAction S (Localization M) where
   smul_zero s := by simp only [← Localization.mk_zero 1, Localization.smul_mk, smul_zero]
   smul_add s x y :=
     Localization.induction_on₂ x y <|
@@ -988,8 +984,7 @@ instance {S : Type*} [Semiring S] [Module S R] [IsScalarTower S R R] : Module S
           intros
           simp only [Localization.smul_mk, add_smul, add_mk_self] }
 
-instance algebra {S : Type*} [CommSemiring S] [Algebra S R] : Algebra S (Localization M)
-    where
+instance algebra {S : Type*} [CommSemiring S] [Algebra S R] : Algebra S (Localization M) where
   toRingHom :=
     RingHom.comp
       { Localization.monoidOf M with
@@ -1105,7 +1100,7 @@ namespace Localization
 
 /-- Negation in a ring localization is defined as `-⟨a, b⟩ = ⟨-a, b⟩`. -/
 protected irreducible_def neg (z : Localization M) : Localization M :=
-  Localization.liftOn z (fun a b => mk (-a) b) @fun a b c d h =>
+  Localization.liftOn z (fun a b => mk (-a) b) fun {a b c d} h =>
     mk_eq_mk_iff.2
       (by
         rw [r_eq_r'] at h ⊢
@@ -1234,8 +1229,7 @@ See note [reducible non-instances]. -/
 @[reducible]
 theorem noZeroDivisors_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [IsLocalization M S]
     (hM : M ≤ nonZeroDivisors A) : NoZeroDivisors S :=
-  {
-    eq_zero_or_eq_zero_of_mul_eq_zero := by
+  { eq_zero_or_eq_zero_of_mul_eq_zero := by
       intro z w h
       cases' surj M z with x hx
       cases' surj M w with y hy

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

This has nice performance benefits.

@@ -90,9 +90,9 @@ open BigOperators
 
 section CommSemiring
 
-variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemiring S]
+variable {R : Type*} [CommSemiring R] (M : Submonoid R) (S : Type*) [CommSemiring S]
 
-variable [Algebra R S] {P : Type _} [CommSemiring P]
+variable [Algebra R S] {P : Type*} [CommSemiring P]
 
 /-- The typeclass `IsLocalization (M : Submodule R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
@@ -597,7 +597,7 @@ theorem lift_injective_iff :
 
 section Map
 
-variable {T : Submonoid P} {Q : Type _} [CommSemiring Q] (hy : M ≤ T.comap g)
+variable {T : Submonoid P} {Q : Type*} [CommSemiring Q] (hy : M ≤ T.comap g)
 
 variable [Algebra P Q] [IsLocalization T Q]
 
@@ -635,7 +635,7 @@ theorem map_mk' (x) (y : M) : map Q g hy (mk' S x y) = mk' Q (g x) ⟨g y, hy y.
 
 --Porting note: new theorem
 @[simp]
-theorem map_id_mk' {Q : Type _} [CommSemiring Q] [Algebra R Q] [IsLocalization M Q] (x) (y : M) :
+theorem map_id_mk' {Q : Type*} [CommSemiring Q] [Algebra R Q] [IsLocalization M Q] (x) (y : M) :
     map Q (RingHom.id R) (le_refl M) (mk' S x y) = mk' Q x y :=
   map_mk' _ _ _
 
@@ -652,7 +652,7 @@ theorem map_unique (j : S →+* Q) (hj : ∀ x : R, j (algebraMap R S x) = algeb
 
 /-- If `CommSemiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
-theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W]
+theorem map_comp_map {A : Type*} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W]
     [Algebra A W] [IsLocalization U W] {l : P →+* A} (hl : T ≤ U.comap l) :
     (map W l hl).comp (map Q g hy : S →+* _) = map W (l.comp g) fun _ hx => hl (hy hx) :=
   RingHom.ext fun x =>
@@ -662,7 +662,7 @@ theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSe
 
 /-- If `CommSemiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
 of the induced maps equals the map of localizations induced by `l ∘ g`. -/
-theorem map_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W] [Algebra A W]
+theorem map_map {A : Type*} [CommSemiring A] {U : Submonoid A} {W} [CommSemiring W] [Algebra A W]
     [IsLocalization U W] {l : P →+* A} (hl : T ≤ U.comap l) (x : S) :
     map W l hl (map Q g hy x) = map W (l.comp g) (fun x hx => hl (hy hx)) x := by
   rw [← map_comp_map (Q := Q) hy hl]; rfl
@@ -722,7 +722,7 @@ end Map
 
 section AlgEquiv
 
-variable {Q : Type _} [CommSemiring Q] [Algebra R Q] [IsLocalization M Q]
+variable {Q : Type*} [CommSemiring Q] [Algebra R Q] [IsLocalization M Q]
 
 section
 
@@ -946,7 +946,7 @@ def mkAddMonoidHom (b : M) : R →+ Localization M
   map_add' _ _ := (add_mk_self _ _ _).symm
 #align localization.mk_add_monoid_hom Localization.mkAddMonoidHom
 
-theorem mk_sum {ι : Type _} (f : ι → R) (s : Finset ι) (b : M) :
+theorem mk_sum {ι : Type*} (f : ι → R) (s : Finset ι) (b : M) :
     mk (∑ i in s, f i) b = ∑ i in s, mk (f i) b :=
   (mkAddMonoidHom b).map_sum f s
 #align localization.mk_sum Localization.mk_sum
@@ -959,7 +959,7 @@ theorem mk_multiset_sum (l : Multiset R) (b : M) : mk l.sum b = (l.map fun a =>
   (mkAddMonoidHom b).map_multiset_sum l
 #align localization.mk_multiset_sum Localization.mk_multiset_sum
 
-instance {S : Type _} [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] :
+instance {S : Type*} [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] :
     DistribMulAction S (Localization M)
     where
   smul_zero s := by simp only [← Localization.mk_zero 1, Localization.smul_mk, smul_zero]
@@ -970,12 +970,12 @@ instance {S : Type _} [Monoid S] [DistribMulAction S R] [IsScalarTower S R R] :
           simp only [Localization.smul_mk, Localization.add_mk, smul_add, mul_comm _ (s • _),
             mul_comm _ r₁, mul_comm _ r₂, smul_mul_assoc]
 
-instance {S : Type _} [Semiring S] [MulSemiringAction S R] [IsScalarTower S R R] :
+instance {S : Type*} [Semiring S] [MulSemiringAction S R] [IsScalarTower S R R] :
     MulSemiringAction S (Localization M) :=
   { inferInstanceAs (MulDistribMulAction S (Localization M)),
     inferInstanceAs (DistribMulAction S (Localization M)) with }
 
-instance {S : Type _} [Semiring S] [Module S R] [IsScalarTower S R R] : Module S (Localization M) :=
+instance {S : Type*} [Semiring S] [Module S R] [IsScalarTower S R R] : Module S (Localization M) :=
   { inferInstanceAs (DistribMulAction S (Localization M)) with
     zero_smul :=
       Localization.ind <|
@@ -988,7 +988,7 @@ instance {S : Type _} [Semiring S] [Module S R] [IsScalarTower S R R] : Module S
           intros
           simp only [Localization.smul_mk, add_smul, add_mk_self] }
 
-instance algebra {S : Type _} [CommSemiring S] [Algebra S R] : Algebra S (Localization M)
+instance algebra {S : Type*} [CommSemiring S] [Algebra S R] : Algebra S (Localization M)
     where
   toRingHom :=
     RingHom.comp
@@ -1043,7 +1043,7 @@ theorem mk_eq_mk' : (mk : R → M → Localization M) = IsLocalization.mk' (Loca
   mk_eq_monoidOf_mk'
 #align localization.mk_eq_mk' Localization.mk_eq_mk'
 
-theorem mk_algebraMap {A : Type _} [CommSemiring A] [Algebra A R] (m : A) :
+theorem mk_algebraMap {A : Type*} [CommSemiring A] [Algebra A R] (m : A) :
     mk (algebraMap A R m) 1 = algebraMap A (Localization M) m := by
   rw [mk_eq_mk', mk'_eq_iff_eq_mul, Submonoid.coe_one, map_one, mul_one]; rfl
 #align localization.mk_algebra_map Localization.mk_algebraMap
@@ -1097,9 +1097,9 @@ end CommSemiring
 
 section CommRing
 
-variable {R : Type _} [CommRing R] {M : Submonoid R} (S : Type _) [CommRing S]
+variable {R : Type*} [CommRing R] {M : Submonoid R} (S : Type*) [CommRing S]
 
-variable [Algebra R S] {P : Type _} [CommRing P]
+variable [Algebra R S] {P : Type*} [CommRing P]
 
 namespace Localization
 
@@ -1166,7 +1166,7 @@ end Localization
 
 namespace IsLocalization
 
-variable {K : Type _} [IsLocalization M S]
+variable {K : Type*} [IsLocalization M S]
 
 theorem to_map_eq_zero_iff {x : R} (hM : M ≤ nonZeroDivisors R) : algebraMap R S x = 0 ↔ x = 0 := by
   rw [← (algebraMap R S).map_zero]
@@ -1205,7 +1205,7 @@ theorem sec_fst_ne_zero [Nontrivial R] [NoZeroDivisors S] (hM : M ≤ nonZeroDiv
   · exact IsLocalization.injective S hM
 #align is_localization.sec_fst_ne_zero IsLocalization.sec_fst_ne_zero
 
-variable (S M) (Q : Type _) [CommRing Q] {g : R →+* P} [Algebra P Q]
+variable (S M) (Q : Type*) [CommRing Q] {g : R →+* P} [Algebra P Q]
 
 /-- Injectivity of a map descends to the map induced on localizations. -/
 theorem map_injective_of_injective (hg : Function.Injective g)
@@ -1226,7 +1226,7 @@ theorem map_injective_of_injective (hg : Function.Injective g)
 
 variable {S Q M}
 
-variable (A : Type _) [CommRing A] [IsDomain A]
+variable (A : Type*) [CommRing A] [IsDomain A]
 
 /-- A `CommRing` `S` which is the localization of a ring `R` without zero divisors at a subset of
 non-zero elements does not have zero divisors.
@@ -1276,7 +1276,7 @@ end IsLocalization
 open IsLocalization
 
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
-theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommRing Rₘ]
+theorem IsField.localization_map_bijective {R Rₘ : Type*} [CommRing R] [CommRing Rₘ]
     {M : Submonoid R} (hM : (0 : R) ∉ M) (hR : IsField R) [Algebra R Rₘ] [IsLocalization M Rₘ] :
     Function.Bijective (algebraMap R Rₘ) := by
   letI := hR.toField
@@ -1288,7 +1288,7 @@ theorem IsField.localization_map_bijective {R Rₘ : Type _} [CommRing R] [CommR
 #align is_field.localization_map_bijective IsField.localization_map_bijective
 
 /-- If `R` is a field, then localizing at a submonoid not containing `0` adds no new elements. -/
-theorem Field.localization_map_bijective {K Kₘ : Type _} [Field K] [CommRing Kₘ] {M : Submonoid K}
+theorem Field.localization_map_bijective {K Kₘ : Type*} [Field K] [CommRing Kₘ] {M : Submonoid K}
     (hM : (0 : K) ∉ M) [Algebra K Kₘ] [IsLocalization M Kₘ] :
     Function.Bijective (algebraMap K Kₘ) :=
   (Field.toIsField K).localization_map_bijective hM
@@ -1298,7 +1298,7 @@ theorem Field.localization_map_bijective {K Kₘ : Type _} [Field K] [CommRing K
 -- way round causes issues with defeq of instances, so this is actually easier.
 section Algebra
 
-variable {S} {Rₘ Sₘ : Type _} [CommRing Rₘ] [CommRing Sₘ]
+variable {S} {Rₘ Sₘ : Type*} [CommRing Rₘ] [CommRing Sₘ]
 
 variable [Algebra R Rₘ] [IsLocalization M Rₘ]
 

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

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

@@ -857,7 +857,7 @@ open IsLocalization
 
 section
 
-instance [Subsingleton R] : Unique (Localization M) where
+instance instUniqueLocalization [Subsingleton R] : Unique (Localization M) where
   uniq a := show a = mk 1 1 from
     Localization.induction_on a fun _ => by
       congr <;> apply Subsingleton.elim

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>

@@ -424,6 +424,17 @@ theorem mk'_mul_mk'_eq_one' (x : R) (y : M) (h : x ∈ M) : mk' S x y * mk' S (y
   mk'_mul_mk'_eq_one ⟨x, h⟩ _
 #align is_localization.mk'_mul_mk'_eq_one' IsLocalization.mk'_mul_mk'_eq_one'
 
+theorem smul_mk' (x y : R) (m : M) : x • mk' S y m = mk' S (x * y) m  := by
+  nth_rw 2 [← one_mul m]
+  rw [mk'_mul, mk'_one, Algebra.smul_def]
+
+@[simp] theorem smul_mk'_one (x : R) (m : M) : x • mk' S 1 m = mk' S x m := by
+  rw [smul_mk', mul_one]
+
+@[simp] lemma smul_mk'_self {m : M} {r : R} :
+    (m : R) • mk' S r m = algebraMap R S r := by
+  rw [smul_mk', mk'_mul_cancel_left]
+
 section
 
 variable (M)

@@ -1252,7 +1252,7 @@ theorem isDomain_of_le_nonZeroDivisors [Algebra A S] {M : Submonoid A} [IsLocali
 
 variable {A}
 
-/-- The localization at of an integral domain to a set of non-zero elements is an integral domain.
+/-- The localization of an integral domain to a set of non-zero elements is an integral domain.
 See note [reducible non-instances]. -/
 @[reducible]
 theorem isDomain_localization {M : Submonoid A} (hM : M ≤ nonZeroDivisors A) :

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.basic
-! leanprover-community/mathlib commit b69c9a770ecf37eb21f7b8cf4fa00de3b62694ec
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Tower
 import Mathlib.Algebra.Ring.Equiv
@@ -15,6 +10,8 @@ import Mathlib.RingTheory.Ideal.Basic
 import Mathlib.RingTheory.NonZeroDivisors
 import Mathlib.Tactic.Ring
 
+#align_import ring_theory.localization.basic from "leanprover-community/mathlib"@"b69c9a770ecf37eb21f7b8cf4fa00de3b62694ec"
+
 /-!
 # Localizations of commutative rings
 

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

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

@@ -899,7 +899,7 @@ local macro "localization_tac" : tactic =>
      simp only [add_mk, Localization.mk_mul, ← Localization.mk_zero 1]
      refine mk_eq_mk_iff.mpr (r_of_eq ?_)
      simp only [Submonoid.coe_mul]
-     ring  })
+     ring })
 
 instance : CommSemiring (Localization M) :=
   { (show CommMonoidWithZero (Localization M) by infer_instance) with

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Matthew Robert Ballard <100034030+mattrobball@users.noreply.github.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -980,7 +980,7 @@ instance {S : Type _} [Semiring S] [Module S R] [IsScalarTower S R R] : Module S
           intros
           simp only [Localization.smul_mk, add_smul, add_mk_self] }
 
-instance {S : Type _} [CommSemiring S] [Algebra S R] : Algebra S (Localization M)
+instance algebra {S : Type _} [CommSemiring S] [Algebra S R] : Algebra S (Localization M)
     where
   toRingHom :=
     RingHom.comp

Changes are of the form

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

@@ -789,7 +789,7 @@ theorem isLocalization_of_base_ringEquiv [IsLocalization M S] (h : R ≃+* P) :
   · intro y
     obtain ⟨⟨x, s⟩, e⟩ := IsLocalization.surj M y
     refine' ⟨⟨h x, _, _, s.prop, rfl⟩, _⟩
-    dsimp only [RingHom.algebraMap_toAlgebra, RingHom.comp_apply] at e⊢
+    dsimp only [RingHom.algebraMap_toAlgebra, RingHom.comp_apply] at e ⊢
     convert e <;> exact h.symm_apply_apply _
   · intro x y
     rw [RingHom.algebraMap_toAlgebra, RingHom.comp_apply, RingHom.comp_apply,
@@ -864,7 +864,7 @@ protected irreducible_def add (z w : Localization M) : Localization M :=
     @fun a a' b b' c c' d d' h1 h2 =>
     mk_eq_mk_iff.2
       (by
-        rw [r_eq_r'] at h1 h2⊢
+        rw [r_eq_r'] at h1 h2 ⊢
         cases' h1 with t₅ ht₅
         cases' h2 with t₆ ht₆
         use t₅ * t₆
@@ -1100,7 +1100,7 @@ protected irreducible_def neg (z : Localization M) : Localization M :=
   Localization.liftOn z (fun a b => mk (-a) b) @fun a b c d h =>
     mk_eq_mk_iff.2
       (by
-        rw [r_eq_r'] at h⊢
+        rw [r_eq_r'] at h ⊢
         cases' h with t ht
         use t
         rw [mul_neg, mul_neg, ht]

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

@@ -100,7 +100,7 @@ variable [Algebra R S] {P : Type _} [CommSemiring P]
 /-- The typeclass `IsLocalization (M : Submodule R) S` where `S` is an `R`-algebra
 expresses that `S` is isomorphic to the localization of `R` at `M`. -/
 class IsLocalization : Prop where
---Porting note: add ' to fields, and made new versions of these with either `S` or `M` explicit.
+  --Porting note: add ' to fields, and made new versions of these with either `S` or `M` explicit.
   /-- Everything in the image of `algebraMap` is a unit -/
   map_units' : ∀ y : M, IsUnit (algebraMap R S y)
   /-- the `algebraMap` is surjective -/
@@ -298,7 +298,7 @@ theorem mk'_add_eq_iff_add_mul_eq_mul {x} {y : M} {z₁ z₂} :
 
 variable (M)
 
-theorem mk'_surjective (z : S) : ∃ (x : _)(y : M), mk' S x y = z :=
+theorem mk'_surjective (z : S) : ∃ (x : _) (y : M), mk' S x y = z :=
   let ⟨r, hr⟩ := IsLocalization.surj _ z
   ⟨r.1, r.2, (eq_mk'_iff_mul_eq.2 hr).symm⟩
 #align is_localization.mk'_surjective IsLocalization.mk'_surjective

These are all doc fixes

@@ -61,7 +61,7 @@ structure with an isomorphic one; one way around this is to isolate a predicate
 a structure up to isomorphism, and reason about things that satisfy the predicate.
 
 A previous version of this file used a fully bundled type of ring localization maps,
-then used a type synonym `f.codomain` for `f : :ocalizationMap M S` to instantiate the
+then used a type synonym `f.codomain` for `f : LocalizationMap M S` to instantiate the
 `R`-algebra structure on `S`. This results in defining ad-hoc copies for everything already
 defined on `S`. By making `IsLocalization` a predicate on the `algebraMap R S`,
 we can ensure the localization map commutes nicely with other `algebraMap`s.

This fixes a bunch of spacing bugs in tactics. Mathlib counterpart of:

• Lean: leanprover/lean4#2240
• Std: leanprover/std4#149
• Aesop: JLimperg/aesop#56

@@ -893,7 +893,7 @@ theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b
   ring
 #align localization.add_mk_self Localization.add_mk_self
 
-local macro "localization_tac": tactic =>
+local macro "localization_tac" : tactic =>
   `(tactic|
    { intros
      simp only [add_mk, Localization.mk_mul, ← Localization.mk_zero 1]

Please feel free to push changes to this branch.

Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>

@@ -1005,7 +1005,7 @@ instance {S : Type _} [CommSemiring S] [Algebra S R] : Algebra S (Localization M
         simp only [← mk_one_eq_monoidOf_mk, mk_mul, Localization.smul_mk, one_mul, mul_one,
           Algebra.commutes]
 
-instance : IsLocalization M (Localization M) where
+instance isLocalization : IsLocalization M (Localization M) where
   map_units' := (Localization.monoidOf M).map_units
   surj' := (Localization.monoidOf M).surj
   eq_iff_exists' := (Localization.monoidOf M).eq_iff_exists

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -648,8 +648,8 @@ theorem map_comp_map {A : Type _} [CommSemiring A] {U : Submonoid A} {W} [CommSe
     [Algebra A W] [IsLocalization U W] {l : P →+* A} (hl : T ≤ U.comap l) :
     (map W l hl).comp (map Q g hy : S →+* _) = map W (l.comp g) fun _ hx => hl (hy hx) :=
   RingHom.ext fun x =>
-    @Submonoid.LocalizationMap.map_map _ _ _ _ _ P _ (toLocalizationMap M S) g _ _ _ _ _ _ _ _ _ _
-      (toLocalizationMap U W) l _ x
+    @Submonoid.LocalizationMap.map_map _ _ _ _ _ P _ (toLocalizationMap M S) g _ (fun y => hy y.2)
+      _ _ _ _ _ _ _ _ (toLocalizationMap U W) l (fun w => hl w.2) x
 #align is_localization.map_comp_map IsLocalization.map_comp_map
 
 /-- If `CommSemiring` homs `g : R →+* P, l : P →+* A` induce maps of localizations, the composition
@@ -679,8 +679,7 @@ noncomputable def ringEquivOfRingEquiv (h : R ≃+* P) (H : M.map h.toMonoidHom
     ext
     apply h.symm_apply_apply
   {
-    map Q (h : R →+* P)
-      _ with
+    map Q (h : R →+* P) (M.le_comap_of_map_le (le_of_eq H)) with
     toFun := map Q (h : R →+* P) (M.le_comap_of_map_le (le_of_eq H))
     invFun := map S (h.symm : P →+* R) (T.le_comap_of_map_le (le_of_eq H'))
     left_inv := fun x => by
@@ -701,14 +700,14 @@ theorem ringEquivOfRingEquiv_eq_map {j : R ≃+* P} (H : M.map j.toMonoidHom = T
 
 --Porting note: removed `simp`, `simp` can prove it
 theorem ringEquivOfRingEquiv_eq {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x) :
-    ringEquivOfRingEquiv S Q j H ((algebraMap R S) x) = algebraMap P Q (j x) :=
-  map_eq _ _
+    ringEquivOfRingEquiv S Q j H ((algebraMap R S) x) = algebraMap P Q (j x) := by
+  simp
 #align is_localization.ring_equiv_of_ring_equiv_eq IsLocalization.ringEquivOfRingEquiv_eq
 
 theorem ringEquivOfRingEquiv_mk' {j : R ≃+* P} (H : M.map j.toMonoidHom = T) (x : R) (y : M) :
     ringEquivOfRingEquiv S Q j H (mk' S x y) =
-      mk' Q (j x) ⟨j y, show j y ∈ T from H ▸ Set.mem_image_of_mem j y.2⟩ :=
-  map_mk' _ _ _
+      mk' Q (j x) ⟨j y, show j y ∈ T from H ▸ Set.mem_image_of_mem j y.2⟩ := by
+  simp [map_mk']
 #align is_localization.ring_equiv_of_ring_equiv_mk' IsLocalization.ringEquivOfRingEquiv_mk'
 
 end Map
@@ -733,12 +732,11 @@ end
 
 --Porting note: removed `simp`, `simp` can prove it
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
-  map_mk' _ _ _
+  by simp
 #align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'
 
 --Porting note: removed `simp`, `simp` can prove it
-theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) = mk' S x y :=
-  map_mk' _ _ _
+theorem algEquiv_symm_mk' (x : R) (y : M) : (algEquiv M S Q).symm (mk' Q x y) = mk' S x y := by simp
 #align is_localization.alg_equiv_symm_mk' IsLocalization.algEquiv_symm_mk'
 
 end AlgEquiv

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -457,8 +457,8 @@ theorem mk'_add (x₁ x₂ : R) (y₁ y₂ : M) :
 #align is_localization.mk'_add IsLocalization.mk'_add
 
 theorem mul_add_inv_left {g : R →+* P} (h : ∀ y : M, IsUnit (g y)) (y : M) (w z₁ z₂ : P) :
-    w * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) h y)⁻¹ + z₁ = z₂ ↔ w + g y * z₁ = g y * z₂ :=
-  by
+    w * ↑(IsUnit.liftRight (g.toMonoidHom.restrict M) h y)⁻¹ + z₁ =
+    z₂ ↔ w + g y * z₁ = g y * z₂ := by
   rw [mul_comm, ← one_mul z₁, ← Units.inv_mul (IsUnit.liftRight (g.toMonoidHom.restrict M) h y),
     mul_assoc, ← mul_add, Units.inv_mul_eq_iff_eq_mul, Units.inv_mul_cancel_left,
     IsUnit.coe_liftRight]

This name wasn't properly capitalised.

@@ -858,7 +858,7 @@ instance [Subsingleton R] : Unique (Localization M) where
 
 /-- Addition in a ring localization is defined as `⟨a, b⟩ + ⟨c, d⟩ = ⟨b * c + d * a, b * d⟩`.
 
-Should not be confused with `addLocalization.add`, which is defined as
+Should not be confused with `AddLocalization.add`, which is defined as
 `⟨a, b⟩ + ⟨c, d⟩ = ⟨a + c, b + d⟩`.
 -/
 protected irreducible_def add (z w : Localization M) : Localization M :=

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -734,7 +734,6 @@ end
 --Porting note: removed `simp`, `simp` can prove it
 theorem algEquiv_mk' (x : R) (y : M) : algEquiv M S Q (mk' S x y) = mk' Q x y :=
   map_mk' _ _ _
-
 #align is_localization.alg_equiv_mk' IsLocalization.algEquiv_mk'
 
 --Porting note: removed `simp`, `simp` can prove it
@@ -1151,7 +1150,6 @@ theorem sub_mk (a c) (b d) : (mk a b : Localization M) - mk c d =
     _ = mk a b + mk (-c) d := by rw [neg_mk]
     _ = mk (b * -c + d * a) (b * d) := (add_mk _ _ _ _)
     _ = mk (d * a - b * c) (b * d) := by congr; ring
-
 #align localization.sub_mk Localization.sub_mk
 
 theorem mk_int_cast (m : ℤ) : (mk m 1 : Localization M) = m := by

Co-authored-by: Pol_tta <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: EmilieUthaiwat <emiliepathum@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Gabriel Ebner <gebner@gebner.org> Co-authored-by: Violeta Hernández <vi.hdz.p@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -862,7 +862,7 @@ instance [Subsingleton R] : Unique (Localization M) where
 Should not be confused with `addLocalization.add`, which is defined as
 `⟨a, b⟩ + ⟨c, d⟩ = ⟨a + c, b + d⟩`.
 -/
-protected def add (z w : Localization M) : Localization M :=
+protected irreducible_def add (z w : Localization M) : Localization M :=
   Localization.liftOn₂ z w (fun a b c d => mk ((b : R) * c + d * a) (b * d))
     @fun a a' b b' c c' d d' h1 h2 =>
     mk_eq_mk_iff.2
@@ -886,12 +886,9 @@ instance : Add (Localization M) :=
 theorem add_mk (a b c d) : (mk a b : Localization M) + mk c d =
     mk ((b : R) * c + (d : R) * a) (b * d) := by
   show Localization.add (mk a b) (mk c d) = mk _ _
-  simp [Localization.add]
+  simp [Localization.add_def]
 #align localization.add_mk Localization.add_mk
 
---Porting note: `Localization.add` was an `irreducible_def`, but then I couldn't prove `add_mk`
-attribute [irreducible] Localization.add
-
 theorem add_mk_self (a b c) : (mk a b : Localization M) + mk c b = mk (a + c) b := by
   rw [add_mk, mk_eq_mk_iff, r_eq_r']
   refine' (r' M).symm ⟨1, _⟩
@@ -1102,7 +1099,7 @@ variable [Algebra R S] {P : Type _} [CommRing P]
 namespace Localization
 
 /-- Negation in a ring localization is defined as `-⟨a, b⟩ = ⟨-a, b⟩`. -/
-protected def neg (z : Localization M) : Localization M :=
+protected irreducible_def neg (z : Localization M) : Localization M :=
   Localization.liftOn z (fun a b => mk (-a) b) @fun a b c d h =>
     mk_eq_mk_iff.2
       (by
@@ -1118,12 +1115,10 @@ instance : Neg (Localization M) :=
 
 theorem neg_mk (a b) : -(mk a b : Localization M) = mk (-a) b := by
   show Localization.neg (mk a b) = mk (-a) b
+  rw [Localization.neg_def]
   apply liftOn_mk
 #align localization.neg_mk Localization.neg_mk
 
---Porting note: `Localization.neg` was an `irreducible_def`, but then I couldn't prove `neg_mk`
-attribute [irreducible] Localization.neg
-
 instance : CommRing (Localization M) :=
   { inferInstanceAs (CommSemiring (Localization M)) with
     zsmul := (· • ·)

@@ -852,14 +852,10 @@ open IsLocalization
 
 section
 
-instance [Subsingleton R] : Unique (Localization M) :=
-  ⟨⟨1⟩, by
-    intro a; refine Localization.induction_on a ?_; intro a;
-    refine Localization.induction_on default ?_
-    intro b;
-    congr
-    exact Subsingleton.elim _ _
-    exact Subsingleton.elim _ _⟩
+instance [Subsingleton R] : Unique (Localization M) where
+  uniq a := show a = mk 1 1 from
+    Localization.induction_on a fun _ => by
+      congr <;> apply Subsingleton.elim
 
 /-- Addition in a ring localization is defined as `⟨a, b⟩ + ⟨c, d⟩ = ⟨b * c + d * a, b * d⟩`.
 

@@ -1408,4 +1408,3 @@ theorem localizationAlgebra_injective (hRS : Function.Injective (algebraMap R S)
 end Algebra
 
 end CommRing
-#lint