ring_theory.ore_localization.basic ⟷ Mathlib.RingTheory.OreLocalization.Basic

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob von Raumer, Kevin Klinge
 -/
 import GroupTheory.MonoidLocalization
-import RingTheory.NonZeroDivisors
+import Algebra.GroupWithZero.NonZeroDivisors
 import RingTheory.OreLocalization.OreSet
 import Tactic.NoncommRing
 

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

@@ -236,8 +236,8 @@ protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
   lift₂Expand mul' fun r₂ p s₂ hp r₁ r s₁ hr =>
     by
     have h₁ := ore_eq r₁ s₂; set r₁' := ore_num r₁ s₂; set s₂' := ore_denom r₁ s₂
-    rcases ore_condition (↑s₂ * r₁') ⟨s₂ * p, hp⟩ with ⟨p', s_star, h₂⟩; dsimp at h₂ 
-    rcases ore_condition r (s₂' * s_star) with ⟨p_flat, s_flat, h₃⟩; simp only [S.coe_mul] at h₃ 
+    rcases ore_condition (↑s₂ * r₁') ⟨s₂ * p, hp⟩ with ⟨p', s_star, h₂⟩; dsimp at h₂
+    rcases ore_condition r (s₂' * s_star) with ⟨p_flat, s_flat, h₃⟩; simp only [S.coe_mul] at h₃
     have : r₁ * r * s_flat = s₂ * p * (p' * p_flat) := by
       rw [← mul_assoc, ← h₂, ← h₁, mul_assoc, h₃]; simp only [mul_assoc]
     rw [mul'_char (r₂ * p) (r₁ * r) ⟨↑s₂ * p, hp⟩ ⟨↑s₁ * r, hr⟩ _ _ this]; clear this
@@ -521,9 +521,9 @@ protected def localizationMap : S.LocalizationMap R[S⁻¹]
   eq_iff_exists' r₁ r₂ := by
     dsimp; constructor
     · intro h
-      rw [numerator_hom_apply, numerator_hom_apply, ore_div_eq_iff] at h 
-      rcases h with ⟨u, v, h₁, h₂⟩; dsimp at h₂ 
-      rw [one_mul, one_mul] at h₂ 
+      rw [numerator_hom_apply, numerator_hom_apply, ore_div_eq_iff] at h
+      rcases h with ⟨u, v, h₁, h₂⟩; dsimp at h₂
+      rw [one_mul, one_mul] at h₂
       subst h₂
       use u
       simpa only [mul_comm] using h₁.symm
@@ -684,7 +684,7 @@ protected theorem add_assoc (x y z : R[S⁻¹]) : x + y + z = x + (y + z) :=
   repeat' rw [← add_ore_div]
   congr 1
   · rcases ore_condition (sd : R) (sa * sc) with ⟨re, se, he⟩
-    · simp_rw [← Submonoid.coe_mul] at hb hc hd 
+    · simp_rw [← Submonoid.coe_mul] at hb hc hd
       assoc_rw [Subtype.coe_eq_of_eq_mk hc]
       rw [← OreLocalization.expand, Subtype.coe_eq_of_eq_mk hd, ← mul_assoc, ←
         OreLocalization.expand, Subtype.coe_eq_of_eq_mk hb]
@@ -693,7 +693,7 @@ protected theorem add_assoc (x y z : R[S⁻¹]) : x + y + z = x + (y + z) :=
   ·
     rw [← OreLocalization.expand', ← mul_assoc, ← mul_assoc, ← OreLocalization.expand', ←
       OreLocalization.expand']
-  · simp_rw [← Submonoid.coe_mul] at ha hd 
+  · simp_rw [← Submonoid.coe_mul] at ha hd
     rw [Subtype.coe_eq_of_eq_mk hd, ← mul_assoc, ← mul_assoc, ← mul_assoc, ← OreLocalization.expand,
       ← OreLocalization.expand', Subtype.coe_eq_of_eq_mk ha, ← OreLocalization.expand]
     apply OreLocalization.expand'
@@ -791,7 +791,7 @@ theorem right_distrib (x y z : R[S⁻¹]) : (x + y) * z = x * z + y * z :=
   induction' x using OreLocalization.ind with r₁ s₁
   induction' y using OreLocalization.ind with r₂ s₂
   induction' z using OreLocalization.ind with r₃ s₃
-  rcases ore_div_add_char' r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩; rw [ha']; clear ha'; norm_cast at ha 
+  rcases ore_div_add_char' r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩; rw [ha']; clear ha'; norm_cast at ha
   rw [OreLocalization.expand' r₁ s₁ sa]
   rw [OreLocalization.expand r₂ s₂ ra (by rw [← ha] <;> apply SetLike.coe_mem)]
   rw [← Subtype.coe_eq_of_eq_mk ha]
@@ -837,7 +837,7 @@ def universalHom : R[S⁻¹] →+* T :=
       rw [add_mul, ← mul_assoc, mul_assoc (f r₁), hf, ← Units.val_mul]
       simp only [mul_one, mul_right_inv, Units.val_one]
       congr 1; rw [mul_assoc]; congr 1
-      norm_cast at h₃ ; have h₃' := Subtype.coe_eq_of_eq_mk h₃
+      norm_cast at h₃; have h₃' := Subtype.coe_eq_of_eq_mk h₃
       rw [← Units.val_mul, ← mul_inv_rev, ← fS.map_mul, h₃']
       have hs₂r₃ : ↑s₂ * r₃ ∈ S := by rw [← h₃]; exact SetLike.coe_mem (s₁ * s₃)
       apply (Units.inv_mul_cancel_left (fS s₂) _).symm.trans
@@ -920,17 +920,17 @@ open scoped nonZeroDivisors
 theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom : R → R[S⁻¹]) :=
   fun r₁ r₂ h =>
   by
-  rw [numerator_hom_apply, numerator_hom_apply, ore_div_eq_iff] at h 
+  rw [numerator_hom_apply, numerator_hom_apply, ore_div_eq_iff] at h
   rcases h with ⟨u, v, h₁, h₂⟩
-  simp only [S.coe_one, one_mul] at h₂ 
-  rwa [← h₂, mul_cancel_right_mem_nonZeroDivisors (hS (SetLike.coe_mem u)), eq_comm] at h₁ 
+  simp only [S.coe_one, one_mul] at h₂
+  rwa [← h₂, mul_cancel_right_mem_nonZeroDivisors (hS (SetLike.coe_mem u)), eq_comm] at h₁
 #align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_inj
 -/
 
 #print OreLocalization.nontrivial_of_nonZeroDivisors /-
 theorem nontrivial_of_nonZeroDivisors [Nontrivial R] (hS : S ≤ R⁰) : Nontrivial R[S⁻¹] :=
   ⟨⟨0, 1, fun h => by
-      rw [OreLocalization.one_def, OreLocalization.zero_def] at h 
+      rw [OreLocalization.one_def, OreLocalization.zero_def] at h
       apply nonZeroDivisors.coe_ne_zero 1 (numerator_hom_inj hS h).symm⟩⟩
 #align ore_localization.nontrivial_of_non_zero_divisors OreLocalization.nontrivial_of_nonZeroDivisors
 -/

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

@@ -3,10 +3,10 @@ Copyright (c) 2022 Jakob von Raumer. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob von Raumer, Kevin Klinge
 -/
-import Mathbin.GroupTheory.MonoidLocalization
-import Mathbin.RingTheory.NonZeroDivisors
-import Mathbin.RingTheory.OreLocalization.OreSet
-import Mathbin.Tactic.NoncommRing
+import GroupTheory.MonoidLocalization
+import RingTheory.NonZeroDivisors
+import RingTheory.OreLocalization.OreSet
+import Tactic.NoncommRing
 
 #align_import ring_theory.ore_localization.basic from "leanprover-community/mathlib"@"b6da1a0b3e7cd83b1f744c49ce48ef8c6307d2f6"
 

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

@@ -516,7 +516,7 @@ protected def localizationMap : S.LocalizationMap R[S⁻¹]
   map_units' := numerator_isUnit
   surj' z := by
     induction' z using OreLocalization.ind with r s
-    use (r, s); dsimp
+    use(r, s); dsimp
     rw [numerator_hom_apply, numerator_hom_apply]; simp
   eq_iff_exists' r₁ r₂ := by
     dsimp; constructor

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Jakob von Raumer. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob von Raumer, Kevin Klinge
-
-! This file was ported from Lean 3 source module ring_theory.ore_localization.basic
-! leanprover-community/mathlib commit b6da1a0b3e7cd83b1f744c49ce48ef8c6307d2f6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.MonoidLocalization
 import Mathbin.RingTheory.NonZeroDivisors
 import Mathbin.RingTheory.OreLocalization.OreSet
 import Mathbin.Tactic.NoncommRing
 
+#align_import ring_theory.ore_localization.basic from "leanprover-community/mathlib"@"b6da1a0b3e7cd83b1f744c49ce48ef8c6307d2f6"
+
 /-!
 
 # Localization over right Ore sets.

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

@@ -52,6 +52,7 @@ namespace OreLocalization
 
 variable (R : Type _) [Monoid R] (S : Submonoid R) [OreSet S]
 
+#print OreLocalization.oreEqv /-
 /-- The setoid on `R × S` used for the Ore localization. -/
 def oreEqv : Setoid (R × S)
     where
@@ -74,6 +75,7 @@ def oreEqv : Setoid (R × S)
       · assoc_rw [hur₂, h, hur₁, mul_assoc]
       · assoc_rw [hs₂u, h, hs₁u, mul_assoc]
 #align ore_localization.ore_eqv OreLocalization.oreEqv
+-/
 
 end OreLocalization
 
@@ -92,42 +94,51 @@ variable {R : Type _} [Monoid R] {S : Submonoid R}
 
 variable (R S) [OreSet S]
 
--- mathport name: «expr [ ⁻¹]»
 notation:1075 R "[" S "⁻¹]" => OreLocalization R S
 
 attribute [local instance] ore_eqv
 
 variable {R S}
 
+#print OreLocalization.oreDiv /-
 /-- The division in the ore localization `R[S⁻¹]`, as a fraction of an element of `R` and `S`. -/
 def oreDiv (r : R) (s : S) : R[S⁻¹] :=
   Quotient.mk' (r, s)
 #align ore_localization.ore_div OreLocalization.oreDiv
+-/
 
--- mathport name: «expr /ₒ »
 infixl:70 " /ₒ " => oreDiv
 
+#print OreLocalization.ind /-
 @[elab_as_elim]
 protected theorem ind {β : R[S⁻¹] → Prop} (c : ∀ (r : R) (s : S), β (r /ₒ s)) : ∀ q, β q := by
   apply Quotient.ind; rintro ⟨r, s⟩; exact c r s
 #align ore_localization.ind OreLocalization.ind
+-/
 
+#print OreLocalization.oreDiv_eq_iff /-
 theorem oreDiv_eq_iff {r₁ r₂ : R} {s₁ s₂ : S} :
     r₁ /ₒ s₁ = r₂ /ₒ s₂ ↔ ∃ (u : S) (v : R), r₂ * u = r₁ * v ∧ (s₂ : R) * u = s₁ * v :=
   Quotient.eq''
 #align ore_localization.ore_div_eq_iff OreLocalization.oreDiv_eq_iff
+-/
 
+#print OreLocalization.expand /-
 /-- A fraction `r /ₒ s` is equal to its expansion by an arbitrary factor `t` if `s * t ∈ S`. -/
 protected theorem expand (r : R) (s : S) (t : R) (hst : (s : R) * t ∈ S) :
     r /ₒ s = r * t /ₒ ⟨s * t, hst⟩ := by apply Quotient.sound;
   refine' ⟨s, t * s, _, _⟩ <;> dsimp <;> rw [mul_assoc] <;> rfl
 #align ore_localization.expand OreLocalization.expand
+-/
 
+#print OreLocalization.expand' /-
 /-- A fraction is equal to its expansion by an factor from s. -/
 protected theorem expand' (r : R) (s s' : S) : r /ₒ s = r * s' /ₒ (s * s') :=
   OreLocalization.expand r s s' (by norm_cast <;> apply SetLike.coe_mem)
 #align ore_localization.expand' OreLocalization.expand'
+-/
 
+#print OreLocalization.eq_of_num_factor_eq /-
 /-- Fractions which differ by a factor of the numerator can be proven equal if
 those factors expand to equal elements of `R`. -/
 protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t = r' * t) :
@@ -145,7 +156,9 @@ protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t
     _ = r₁ * r' * r₂ * t' /ₒ (s * t') := by simp [← mul_assoc]
     _ = r₁ * r' * r₂ /ₒ s := by symm <;> apply OreLocalization.expand
 #align ore_localization.eq_of_num_factor_eq OreLocalization.eq_of_num_factor_eq
+-/
 
+#print OreLocalization.liftExpand /-
 /-- A function or predicate over `R` and `S` can be lifted to `R[S⁻¹]` if it is invariant
 under expansion on the right. -/
 def liftExpand {C : Sort _} (P : R → S → C)
@@ -159,14 +172,18 @@ def liftExpand {C : Sort _} (P : R → S → C)
     rw [hP r₁ v s₁ s₁vS, hP r₂ u s₂ (by norm_cast; rw [hs₂]; assumption), hr₂]
     simpa [← hs₂]
 #align ore_localization.lift_expand OreLocalization.liftExpand
+-/
 
+#print OreLocalization.liftExpand_of /-
 @[simp]
 theorem liftExpand_of {C : Sort _} {P : R → S → C}
     {hP : ∀ (r t : R) (s : S) (ht : (s : R) * t ∈ S), P r s = P (r * t) ⟨s * t, ht⟩} (r : R)
     (s : S) : liftExpand P hP (r /ₒ s) = P r s :=
   rfl
 #align ore_localization.lift_expand_of OreLocalization.liftExpand_of
+-/
 
+#print OreLocalization.lift₂Expand /-
 /-- A version of `lift_expand` used to simultaneously lift functions with two arguments
 in ``R[S⁻¹]`.-/
 def lift₂Expand {C : Sort _} (P : R → S → R → S → C)
@@ -182,7 +199,9 @@ def lift₂Expand {C : Sort _} (P : R → S → R → S → C)
     ext x; induction' x using OreLocalization.ind with r₂ s₂
     rw [lift_expand_of, lift_expand_of, hP r₁ t₁ s₁ ht₁ r₂ 1 s₂ (by simp)]; simp
 #align ore_localization.lift₂_expand OreLocalization.lift₂Expand
+-/
 
+#print OreLocalization.lift₂Expand_of /-
 @[simp]
 theorem lift₂Expand_of {C : Sort _} {P : R → S → R → S → C}
     {hP :
@@ -192,6 +211,7 @@ theorem lift₂Expand_of {C : Sort _} {P : R → S → R → S → C}
     (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) : lift₂Expand P hP (r₁ /ₒ s₁) (r₂ /ₒ s₂) = P r₁ s₁ r₂ s₂ :=
   rfl
 #align ore_localization.lift₂_expand_of OreLocalization.lift₂Expand_of
+-/
 
 private def mul' (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) : R[S⁻¹] :=
   r₁ * oreNum r₂ s₁ /ₒ (s₂ * oreDenom r₂ s₁)
@@ -243,56 +263,72 @@ protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
 instance : Mul R[S⁻¹] :=
   ⟨OreLocalization.mul⟩
 
+#print OreLocalization.oreDiv_mul_oreDiv /-
 theorem oreDiv_mul_oreDiv {r₁ r₂ : R} {s₁ s₂ : S} :
     r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r₁ * oreNum r₂ s₁ /ₒ (s₂ * oreDenom r₂ s₁) :=
   rfl
 #align ore_localization.ore_div_mul_ore_div OreLocalization.oreDiv_mul_oreDiv
+-/
 
+#print OreLocalization.oreDiv_mul_char /-
 /-- A characterization lemma for the multiplication on the Ore localization, allowing for a choice
 of Ore numerator and Ore denominator. -/
 theorem oreDiv_mul_char (r₁ r₂ : R) (s₁ s₂ : S) (r' : R) (s' : S) (huv : r₂ * (s' : R) = s₁ * r') :
     r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r₁ * r' /ₒ (s₂ * s') :=
   mul'_char r₁ r₂ s₁ s₂ s' r' huv
 #align ore_localization.ore_div_mul_char OreLocalization.oreDiv_mul_char
+-/
 
+#print OreLocalization.oreDivMulChar' /-
 /-- Another characterization lemma for the multiplication on the Ore localizaion delivering
 Ore witnesses and conditions bundled in a sigma type. -/
 def oreDivMulChar' (r₁ r₂ : R) (s₁ s₂ : S) :
     Σ' r' : R, Σ' s' : S, r₂ * (s' : R) = s₁ * r' ∧ r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r₁ * r' /ₒ (s₂ * s') :=
   ⟨oreNum r₂ s₁, oreDenom r₂ s₁, ore_eq r₂ s₁, oreDiv_mul_oreDiv⟩
 #align ore_localization.ore_div_mul_char' OreLocalization.oreDivMulChar'
+-/
 
 instance : One R[S⁻¹] :=
   ⟨1 /ₒ 1⟩
 
+#print OreLocalization.one_def /-
 protected theorem one_def : (1 : R[S⁻¹]) = 1 /ₒ 1 :=
   rfl
 #align ore_localization.one_def OreLocalization.one_def
+-/
 
 instance : Inhabited R[S⁻¹] :=
   ⟨1⟩
 
+#print OreLocalization.div_eq_one' /-
 @[simp]
 protected theorem div_eq_one' {r : R} (hr : r ∈ S) : r /ₒ ⟨r, hr⟩ = 1 := by
   rw [OreLocalization.one_def, ore_div_eq_iff]; exact ⟨⟨r, hr⟩, 1, by simp, by simp⟩
 #align ore_localization.div_eq_one' OreLocalization.div_eq_one'
+-/
 
+#print OreLocalization.div_eq_one /-
 @[simp]
 protected theorem div_eq_one {s : S} : (s : R) /ₒ s = 1 := by
   cases s <;> apply OreLocalization.div_eq_one'
 #align ore_localization.div_eq_one OreLocalization.div_eq_one
+-/
 
+#print OreLocalization.one_mul /-
 protected theorem one_mul (x : R[S⁻¹]) : 1 * x = x :=
   by
   induction' x using OreLocalization.ind with r s
   simp [OreLocalization.one_def, ore_div_mul_char (1 : R) r (1 : S) s r 1 (by simp)]
 #align ore_localization.one_mul OreLocalization.one_mul
+-/
 
+#print OreLocalization.mul_one /-
 protected theorem mul_one (x : R[S⁻¹]) : x * 1 = x :=
   by
   induction' x using OreLocalization.ind with r s
   simp [OreLocalization.one_def, ore_div_mul_char r 1 s 1 1 s (by simp)]
 #align ore_localization.mul_one OreLocalization.mul_one
+-/
 
 #print OreLocalization.mul_assoc /-
 protected theorem mul_assoc (x y z : R[S⁻¹]) : x * y * z = x * (y * z) :=
@@ -318,31 +354,42 @@ instance : Monoid R[S⁻¹] :=
     mul_one := OreLocalization.mul_one
     mul_assoc := OreLocalization.mul_assoc }
 
+#print OreLocalization.mul_inv /-
 protected theorem mul_inv (s s' : S) : (s : R) /ₒ s' * (s' /ₒ s) = 1 := by
   simp [ore_div_mul_char (s : R) s' s' s 1 1 (by simp)]
 #align ore_localization.mul_inv OreLocalization.mul_inv
+-/
 
+#print OreLocalization.mul_one_div /-
 @[simp]
 protected theorem mul_one_div {r : R} {s t : S} : r /ₒ s * (1 /ₒ t) = r /ₒ (t * s) := by
   simp [ore_div_mul_char r 1 s t 1 s (by simp)]
 #align ore_localization.mul_one_div OreLocalization.mul_one_div
+-/
 
+#print OreLocalization.mul_cancel /-
 @[simp]
 protected theorem mul_cancel {r : R} {s t : S} : r /ₒ s * (s /ₒ t) = r /ₒ t := by
   simp [ore_div_mul_char r s s t 1 1 (by simp)]
 #align ore_localization.mul_cancel OreLocalization.mul_cancel
+-/
 
+#print OreLocalization.mul_cancel' /-
 @[simp]
 protected theorem mul_cancel' {r₁ r₂ : R} {s t : S} : r₁ /ₒ s * (s * r₂ /ₒ t) = r₁ * r₂ /ₒ t := by
   simp [ore_div_mul_char r₁ (s * r₂) s t r₂ 1 (by simp)]
 #align ore_localization.mul_cancel' OreLocalization.mul_cancel'
+-/
 
+#print OreLocalization.div_one_mul /-
 @[simp]
 theorem div_one_mul {p r : R} {s : S} : r /ₒ 1 * (p /ₒ s) = r * p /ₒ s :=
   by--TODO use coercion r ↦ r /ₒ 1
   simp [ore_div_mul_char r p 1 s p 1 (by simp)]
 #align ore_localization.div_one_mul OreLocalization.div_one_mul
+-/
 
+#print OreLocalization.numeratorUnit /-
 /-- The fraction `s /ₒ 1` as a unit in `R[S⁻¹]`, where `s : S`. -/
 def numeratorUnit (s : S) : Units R[S⁻¹]
     where
@@ -351,7 +398,9 @@ def numeratorUnit (s : S) : Units R[S⁻¹]
   val_inv := OreLocalization.mul_inv s 1
   inv_val := OreLocalization.mul_inv 1 s
 #align ore_localization.numerator_unit OreLocalization.numeratorUnit
+-/
 
+#print OreLocalization.numeratorHom /-
 /-- The multiplicative homomorphism from `R` to `R[S⁻¹]`, mapping `r : R` to the
 fraction `r /ₒ 1`. -/
 def numeratorHom : R →* R[S⁻¹] where
@@ -359,14 +408,19 @@ def numeratorHom : R →* R[S⁻¹] where
   map_one' := rfl
   map_mul' r₁ r₂ := div_one_mul.symm
 #align ore_localization.numerator_hom OreLocalization.numeratorHom
+-/
 
+#print OreLocalization.numeratorHom_apply /-
 theorem numeratorHom_apply {r : R} : numeratorHom r = r /ₒ (1 : S) :=
   rfl
 #align ore_localization.numerator_hom_apply OreLocalization.numeratorHom_apply
+-/
 
+#print OreLocalization.numerator_isUnit /-
 theorem numerator_isUnit (s : S) : IsUnit (numeratorHom (s : R) : R[S⁻¹]) :=
   ⟨numeratorUnit s, rfl⟩
 #align ore_localization.numerator_is_unit OreLocalization.numerator_isUnit
+-/
 
 section UMP
 
@@ -376,8 +430,7 @@ variable (f : R →* T) (fS : S →* Units T)
 
 variable (hf : ∀ s : S, f s = fS s)
 
-include f fS hf
-
+#print OreLocalization.universalMulHom /-
 /-- The universal lift from a morphism `R →* T`, which maps elements of `S` to units of `T`,
 to a morphism `R[S⁻¹] →* T`. -/
 def universalMulHom : R[S⁻¹] →* T
@@ -406,16 +459,22 @@ def universalMulHom : R[S⁻¹] →* T
       f.map_mul, mul_assoc, fS.map_mul, ← Units.val_mul]
     rfl
 #align ore_localization.universal_mul_hom OreLocalization.universalMulHom
+-/
 
+#print OreLocalization.universalMulHom_apply /-
 theorem universalMulHom_apply {r : R} {s : S} :
     universalMulHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
   rfl
 #align ore_localization.universal_mul_hom_apply OreLocalization.universalMulHom_apply
+-/
 
+#print OreLocalization.universalMulHom_commutes /-
 theorem universalMulHom_commutes {r : R} : universalMulHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_mul_hom_apply]
 #align ore_localization.universal_mul_hom_commutes OreLocalization.universalMulHom_commutes
+-/
 
+#print OreLocalization.universalMulHom_unique /-
 /-- The universal morphism `universal_mul_hom` is unique. -/
 theorem universalMulHom_unique (φ : R[S⁻¹] →* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
     φ = universalMulHom f fS hf := by
@@ -424,6 +483,7 @@ theorem universalMulHom_unique (φ : R[S⁻¹] →* T) (huniv : ∀ r : R, φ (n
     Units.val_one, ← mul_right_inv (fS s), Units.val_mul, ← mul_assoc, ← hf, ← huniv, ← φ.map_mul,
     numerator_hom_apply, OreLocalization.mul_cancel]
 #align ore_localization.universal_mul_hom_unique OreLocalization.universalMulHom_unique
+-/
 
 end UMP
 
@@ -433,10 +493,12 @@ section CommMonoid
 
 variable {R : Type _} [CommMonoid R] {S : Submonoid R} [OreSet S]
 
+#print OreLocalization.oreDiv_mul_oreDiv_comm /-
 theorem oreDiv_mul_oreDiv_comm {r₁ r₂ : R} {s₁ s₂ : S} :
     r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r₁ * r₂ /ₒ (s₁ * s₂) := by
   rw [ore_div_mul_char r₁ r₂ s₁ s₂ r₂ s₁ (by simp [mul_comm]), mul_comm s₂]
 #align ore_localization.ore_div_mul_ore_div_comm OreLocalization.oreDiv_mul_oreDiv_comm
+-/
 
 instance : CommMonoid R[S⁻¹] :=
   { OreLocalization.monoid with
@@ -447,6 +509,7 @@ instance : CommMonoid R[S⁻¹] :=
 
 variable (R S)
 
+#print OreLocalization.localizationMap /-
 /-- The morphism `numerator_hom` is a monoid localization map in the case of commutative `R`. -/
 protected def localizationMap : S.LocalizationMap R[S⁻¹]
     where
@@ -473,6 +536,7 @@ protected def localizationMap : S.LocalizationMap R[S⁻¹]
       · simpa [mul_comm] using h.symm
       · simp [one_mul]
 #align ore_localization.localization_map OreLocalization.localizationMap
+-/
 
 #print OreLocalization.equivMonoidLocalization /-
 /-- If `R` is commutative, Ore localization and monoid localization are isomorphic. -/
@@ -575,18 +639,23 @@ private def add : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] := fun x =>
 instance : Add R[S⁻¹] :=
   ⟨add⟩
 
+#print OreLocalization.oreDiv_add_oreDiv /-
 theorem oreDiv_add_oreDiv {r r' : R} {s s' : S} :
     r /ₒ s + r' /ₒ s' = (r * oreDenom (s : R) s' + r' * oreNum s s') /ₒ (s * oreDenom s s') :=
   rfl
 #align ore_localization.ore_div_add_ore_div OreLocalization.oreDiv_add_oreDiv
+-/
 
+#print OreLocalization.oreDiv_add_char /-
 /-- A characterization of the addition on the Ore localizaion, allowing for arbitrary Ore
 numerator and Ore denominator. -/
 theorem oreDiv_add_char {r r' : R} (s s' : S) (rb : R) (sb : S) (h : (s : R) * sb = s' * rb) :
     r /ₒ s + r' /ₒ s' = (r * sb + r' * rb) /ₒ (s * sb) :=
   add''_char r s r' s' rb sb h
 #align ore_localization.ore_div_add_char OreLocalization.oreDiv_add_char
+-/
 
+#print OreLocalization.oreDivAddChar' /-
 /-- Another characterization of the addition on the Ore localization, bundling up all witnesses
 and conditions into a sigma type. -/
 def oreDivAddChar' (r r' : R) (s s' : S) :
@@ -595,12 +664,16 @@ def oreDivAddChar' (r r' : R) (s s' : S) :
         (s : R) * s'' = s' * r'' ∧ r /ₒ s + r' /ₒ s' = (r * s'' + r' * r'') /ₒ (s * s'') :=
   ⟨oreNum s s', oreDenom s s', ore_eq s s', oreDiv_add_oreDiv⟩
 #align ore_localization.ore_div_add_char' OreLocalization.oreDivAddChar'
+-/
 
+#print OreLocalization.add_oreDiv /-
 @[simp]
 theorem add_oreDiv {r r' : R} {s : S} : r /ₒ s + r' /ₒ s = (r + r') /ₒ s := by
   simp [ore_div_add_char s s 1 1 (by simp)]
 #align ore_localization.add_ore_div OreLocalization.add_oreDiv
+-/
 
+#print OreLocalization.add_assoc /-
 protected theorem add_assoc (x y z : R[S⁻¹]) : x + y + z = x + (y + z) :=
   by
   induction' x using OreLocalization.ind with r₁ s₁
@@ -628,6 +701,7 @@ protected theorem add_assoc (x y z : R[S⁻¹]) : x + y + z = x + (y + z) :=
       ← OreLocalization.expand', Subtype.coe_eq_of_eq_mk ha, ← OreLocalization.expand]
     apply OreLocalization.expand'
 #align ore_localization.add_assoc OreLocalization.add_assoc
+-/
 
 private def zero : R[S⁻¹] :=
   0 /ₒ 1
@@ -635,27 +709,35 @@ private def zero : R[S⁻¹] :=
 instance : Zero R[S⁻¹] :=
   ⟨zero⟩
 
+#print OreLocalization.zero_def /-
 protected theorem zero_def : (0 : R[S⁻¹]) = 0 /ₒ 1 :=
   rfl
 #align ore_localization.zero_def OreLocalization.zero_def
+-/
 
+#print OreLocalization.zero_div_eq_zero /-
 @[simp]
 theorem zero_div_eq_zero (s : S) : 0 /ₒ s = 0 := by rw [OreLocalization.zero_def, ore_div_eq_iff];
   exact ⟨s, 1, by simp⟩
 #align ore_localization.zero_div_eq_zero OreLocalization.zero_div_eq_zero
+-/
 
+#print OreLocalization.zero_add /-
 protected theorem zero_add (x : R[S⁻¹]) : 0 + x = x :=
   by
   induction x using OreLocalization.ind
   rw [← zero_div_eq_zero, add_ore_div]; simp
 #align ore_localization.zero_add OreLocalization.zero_add
+-/
 
+#print OreLocalization.add_comm /-
 protected theorem add_comm (x y : R[S⁻¹]) : x + y = y + x :=
   by
   induction x using OreLocalization.ind
   induction y using OreLocalization.ind
   change add' _ _ (_ /ₒ _) = _; apply add'_comm
 #align ore_localization.add_comm OreLocalization.add_comm
+-/
 
 instance : AddCommMonoid R[S⁻¹] :=
   { OreLocalization.hasAdd with
@@ -665,18 +747,23 @@ instance : AddCommMonoid R[S⁻¹] :=
     zero_add := OreLocalization.zero_add
     add_zero := fun x => by rw [OreLocalization.add_comm, OreLocalization.zero_add] }
 
+#print OreLocalization.zero_mul /-
 protected theorem zero_mul (x : R[S⁻¹]) : 0 * x = 0 :=
   by
   induction' x using OreLocalization.ind with r s
   rw [OreLocalization.zero_def, ore_div_mul_char 0 r 1 s r 1 (by simp)]; simp
 #align ore_localization.zero_mul OreLocalization.zero_mul
+-/
 
+#print OreLocalization.mul_zero /-
 protected theorem mul_zero (x : R[S⁻¹]) : x * 0 = 0 :=
   by
   induction' x using OreLocalization.ind with r s
   rw [OreLocalization.zero_def, ore_div_mul_char r 0 s 1 0 1 (by simp)]; simp
 #align ore_localization.mul_zero OreLocalization.mul_zero
+-/
 
+#print OreLocalization.left_distrib /-
 protected theorem left_distrib (x y z : R[S⁻¹]) : x * (y + z) = x * y + x * z :=
   by
   induction' x using OreLocalization.ind with r₁ s₁
@@ -699,7 +786,9 @@ protected theorem left_distrib (x y z : R[S⁻¹]) : x * (y + z) = x * y + x * z
     rw [add_mul, S.coe_mul, ← mul_assoc, hb, ← mul_assoc, mul_assoc r₃, hc, mul_assoc, ← mul_add]
   rw [OreLocalization.mul_cancel']; simp only [mul_one, Submonoid.coe_mul, mul_add, ← mul_assoc]
 #align ore_localization.left_distrib OreLocalization.left_distrib
+-/
 
+#print OreLocalization.right_distrib /-
 theorem right_distrib (x y z : R[S⁻¹]) : (x + y) * z = x * z + y * z :=
   by
   induction' x using OreLocalization.ind with r₁ s₁
@@ -711,6 +800,7 @@ theorem right_distrib (x y z : R[S⁻¹]) : (x + y) * z = x * z + y * z :=
   rw [← Subtype.coe_eq_of_eq_mk ha]
   repeat' rw [ore_div_mul_ore_div]; simp only [add_mul, add_ore_div]
 #align ore_localization.right_distrib OreLocalization.right_distrib
+-/
 
 instance : Semiring R[S⁻¹] :=
   { OreLocalization.addCommMonoid,
@@ -728,8 +818,7 @@ variable (f : R →+* T) (fS : S →* Units T)
 
 variable (hf : ∀ s : S, f s = fS s)
 
-include f fS hf
-
+#print OreLocalization.universalHom /-
 /-- The universal lift from a ring homomorphism `f : R →+* T`, which maps elements in `S` to
 units of `T`, to a ring homomorphism `R[S⁻¹] →+* T`. This extends the construction on
 monoids. -/
@@ -770,20 +859,27 @@ def universalHom : R[S⁻¹] →+* T :=
         rw [hf, ← mul_assoc, ← h₃', Units.inv_mul]
       rw [one_mul, ← h₃', Units.mul_inv, mul_one] }
 #align ore_localization.universal_hom OreLocalization.universalHom
+-/
 
+#print OreLocalization.universalHom_apply /-
 theorem universalHom_apply {r : R} {s : S} :
     universalHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
   rfl
 #align ore_localization.universal_hom_apply OreLocalization.universalHom_apply
+-/
 
+#print OreLocalization.universalHom_commutes /-
 theorem universalHom_commutes {r : R} : universalHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_hom_apply]
 #align ore_localization.universal_hom_commutes OreLocalization.universalHom_commutes
+-/
 
+#print OreLocalization.universalHom_unique /-
 theorem universalHom_unique (φ : R[S⁻¹] →+* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
     φ = universalHom f fS hf :=
   RingHom.coe_monoidHom_injective <| universalMulHom_unique (RingHom.toMonoidHom f) fS hf (↑φ) huniv
 #align ore_localization.universal_hom_unique OreLocalization.universalHom_unique
+-/
 
 end UMP
 
@@ -793,23 +889,29 @@ section Ring
 
 variable {R : Type _} [Ring R] {S : Submonoid R} [OreSet S]
 
+#print OreLocalization.neg /-
 /-- Negation on the Ore localization is defined via negation on the numerator. -/
 protected def neg : R[S⁻¹] → R[S⁻¹] :=
   liftExpand (fun (r : R) (s : S) => -r /ₒ s) fun r t s ht => by
     rw [neg_mul_eq_neg_mul, ← OreLocalization.expand]
 #align ore_localization.neg OreLocalization.neg
+-/
 
 instance : Neg R[S⁻¹] :=
   ⟨OreLocalization.neg⟩
 
+#print OreLocalization.neg_def /-
 @[simp]
 protected theorem neg_def (r : R) (s : S) : -(r /ₒ s) = -r /ₒ s :=
   rfl
 #align ore_localization.neg_def OreLocalization.neg_def
+-/
 
+#print OreLocalization.add_left_neg /-
 protected theorem add_left_neg (x : R[S⁻¹]) : -x + x = 0 := by
   induction' x using OreLocalization.ind with r s <;> simp
 #align ore_localization.add_left_neg OreLocalization.add_left_neg
+-/
 
 instance : Ring R[S⁻¹] :=
   { OreLocalization.semiring, OreLocalization.hasNeg with
@@ -817,6 +919,7 @@ instance : Ring R[S⁻¹] :=
 
 open scoped nonZeroDivisors
 
+#print OreLocalization.numeratorHom_inj /-
 theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom : R → R[S⁻¹]) :=
   fun r₁ r₂ h =>
   by
@@ -825,12 +928,15 @@ theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom :
   simp only [S.coe_one, one_mul] at h₂ 
   rwa [← h₂, mul_cancel_right_mem_nonZeroDivisors (hS (SetLike.coe_mem u)), eq_comm] at h₁ 
 #align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_inj
+-/
 
+#print OreLocalization.nontrivial_of_nonZeroDivisors /-
 theorem nontrivial_of_nonZeroDivisors [Nontrivial R] (hS : S ≤ R⁰) : Nontrivial R[S⁻¹] :=
   ⟨⟨0, 1, fun h => by
       rw [OreLocalization.one_def, OreLocalization.zero_def] at h 
       apply nonZeroDivisors.coe_ne_zero 1 (numerator_hom_inj hS h).symm⟩⟩
 #align ore_localization.nontrivial_of_non_zero_divisors OreLocalization.nontrivial_of_nonZeroDivisors
+-/
 
 end Ring
 
@@ -849,6 +955,7 @@ variable [NoZeroDivisors R]
 
 noncomputable section
 
+#print OreLocalization.inv /-
 /-- The inversion of Ore fractions for a ring without zero divisors, satisying `0⁻¹ = 0` and
 `(r /ₒ r')⁻¹ = r' /ₒ r` for `r ≠ 0`. -/
 protected def inv : R[R⁰⁻¹] → R[R⁰⁻¹] :=
@@ -865,17 +972,21 @@ protected def inv : R[R⁰⁻¹] → R[R⁰⁻¹] :=
         · simp only [hr, ht, SetLike.coe_mk, dif_neg, not_false_iff, or_self_iff, mul_eq_zero]
           apply OreLocalization.expand)
 #align ore_localization.inv OreLocalization.inv
+-/
 
 instance : Inv R[R⁰⁻¹] :=
   ⟨OreLocalization.inv⟩
 
+#print OreLocalization.inv_def /-
 protected theorem inv_def {r : R} {s : R⁰} :
     (r /ₒ s)⁻¹ =
       if hr : r = (0 : R) then (0 : R[R⁰⁻¹])
       else s /ₒ ⟨r, fun _ => eq_zero_of_ne_zero_of_mul_right_eq_zero hr⟩ :=
   rfl
 #align ore_localization.inv_def OreLocalization.inv_def
+-/
 
+#print OreLocalization.mul_inv_cancel /-
 protected theorem mul_inv_cancel (x : R[R⁰⁻¹]) (h : x ≠ 0) : x * x⁻¹ = 1 :=
   by
   induction' x using OreLocalization.ind with r s
@@ -884,10 +995,13 @@ protected theorem mul_inv_cancel (x : R[R⁰⁻¹]) (h : x ≠ 0) : x * x⁻¹ =
   · exfalso; apply h; simp [hr]
   · simp [hr]; apply OreLocalization.div_eq_one'
 #align ore_localization.mul_inv_cancel OreLocalization.mul_inv_cancel
+-/
 
+#print OreLocalization.inv_zero /-
 protected theorem inv_zero : (0 : R[R⁰⁻¹])⁻¹ = 0 := by
   rw [OreLocalization.zero_def, OreLocalization.inv_def]; simp
 #align ore_localization.inv_zero OreLocalization.inv_zero
+-/
 
 instance : DivisionRing R[R⁰⁻¹] :=
   { OreLocalization.nontrivial, OreLocalization.hasInv,

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

@@ -144,7 +144,6 @@ protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t
     _ = r₁ * r' * (r₂ * t') /ₒ (s * t') := by rw [hr₂]
     _ = r₁ * r' * r₂ * t' /ₒ (s * t') := by simp [← mul_assoc]
     _ = r₁ * r' * r₂ /ₒ s := by symm <;> apply OreLocalization.expand
-    
 #align ore_localization.eq_of_num_factor_eq OreLocalization.eq_of_num_factor_eq
 
 /-- A function or predicate over `R` and `S` can be lifted to `R[S⁻¹]` if it is invariant
@@ -208,7 +207,6 @@ private theorem mul'_char (r₁ r₂ : R) (s₁ s₂ : S) (u : S) (v : R) (huv :
       (s₁ : R) * (v * r₃) = r₂ * u * r₃ := by assoc_rw [← huv] <;> symm <;> apply mul_assoc
       _ = r₂ * u₀ * s₃ := by assoc_rw [← h₃] <;> rfl
       _ = s₁ * (v₀ * s₃) := by assoc_rw [h₀] <;> apply mul_assoc
-      
   rcases ore_left_cancel _ _ _ this with ⟨s₄, hs₄⟩
   symm; rw [ore_div_eq_iff]
   use s₃ * s₄; use r₃ * s₄; simp only [Submonoid.coe_mul]; constructor

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

@@ -237,7 +237,7 @@ protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
     rw [this]; clear this
     rcases ore_left_cancel (p * p') (r₁' * ↑s_star) s₂ (by simp [← mul_assoc, h₂]) with ⟨s₂'', h₂''⟩
     rw [← mul_assoc, mul_assoc r₂, OreLocalization.eq_of_num_factor_eq h₂'']
-    norm_cast  at hsssp ⊢; rw [← OreLocalization.expand _ _ _ hsssp, ← mul_assoc]
+    norm_cast at hsssp ⊢; rw [← OreLocalization.expand _ _ _ hsssp, ← mul_assoc]
     apply OreLocalization.expand
 #align ore_localization.mul OreLocalization.mul
 -/
@@ -707,8 +707,7 @@ theorem right_distrib (x y z : R[S⁻¹]) : (x + y) * z = x * z + y * z :=
   induction' x using OreLocalization.ind with r₁ s₁
   induction' y using OreLocalization.ind with r₂ s₂
   induction' z using OreLocalization.ind with r₃ s₃
-  rcases ore_div_add_char' r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩; rw [ha']; clear ha';
-  norm_cast  at ha 
+  rcases ore_div_add_char' r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩; rw [ha']; clear ha'; norm_cast at ha 
   rw [OreLocalization.expand' r₁ s₁ sa]
   rw [OreLocalization.expand r₂ s₂ ra (by rw [← ha] <;> apply SetLike.coe_mem)]
   rw [← Subtype.coe_eq_of_eq_mk ha]
@@ -754,7 +753,7 @@ def universalHom : R[S⁻¹] →+* T :=
       rw [add_mul, ← mul_assoc, mul_assoc (f r₁), hf, ← Units.val_mul]
       simp only [mul_one, mul_right_inv, Units.val_one]
       congr 1; rw [mul_assoc]; congr 1
-      norm_cast  at h₃ ; have h₃' := Subtype.coe_eq_of_eq_mk h₃
+      norm_cast at h₃ ; have h₃' := Subtype.coe_eq_of_eq_mk h₃
       rw [← Units.val_mul, ← mul_inv_rev, ← fS.map_mul, h₃']
       have hs₂r₃ : ↑s₂ * r₃ ∈ S := by rw [← h₃]; exact SetLike.coe_mem (s₁ * s₃)
       apply (Units.inv_mul_cancel_left (fS s₂) _).symm.trans

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

@@ -55,7 +55,7 @@ variable (R : Type _) [Monoid R] (S : Submonoid R) [OreSet S]
 /-- The setoid on `R × S` used for the Ore localization. -/
 def oreEqv : Setoid (R × S)
     where
-  R rs rs' := ∃ (u : S)(v : R), rs'.1 * u = rs.1 * v ∧ (rs'.2 : R) * u = rs.2 * v
+  R rs rs' := ∃ (u : S) (v : R), rs'.1 * u = rs.1 * v ∧ (rs'.2 : R) * u = rs.2 * v
   iseqv := by
     refine' ⟨_, _, _⟩
     · rintro ⟨r, s⟩; use 1; use 1; simp [Submonoid.one_mem]
@@ -113,7 +113,7 @@ protected theorem ind {β : R[S⁻¹] → Prop} (c : ∀ (r : R) (s : S), β (r
 #align ore_localization.ind OreLocalization.ind
 
 theorem oreDiv_eq_iff {r₁ r₂ : R} {s₁ s₂ : S} :
-    r₁ /ₒ s₁ = r₂ /ₒ s₂ ↔ ∃ (u : S)(v : R), r₂ * u = r₁ * v ∧ (s₂ : R) * u = s₁ * v :=
+    r₁ /ₒ s₁ = r₂ /ₒ s₂ ↔ ∃ (u : S) (v : R), r₂ * u = r₁ * v ∧ (s₂ : R) * u = s₁ * v :=
   Quotient.eq''
 #align ore_localization.ore_div_eq_iff OreLocalization.oreDiv_eq_iff
 
@@ -221,8 +221,8 @@ protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
   lift₂Expand mul' fun r₂ p s₂ hp r₁ r s₁ hr =>
     by
     have h₁ := ore_eq r₁ s₂; set r₁' := ore_num r₁ s₂; set s₂' := ore_denom r₁ s₂
-    rcases ore_condition (↑s₂ * r₁') ⟨s₂ * p, hp⟩ with ⟨p', s_star, h₂⟩; dsimp at h₂
-    rcases ore_condition r (s₂' * s_star) with ⟨p_flat, s_flat, h₃⟩; simp only [S.coe_mul] at h₃
+    rcases ore_condition (↑s₂ * r₁') ⟨s₂ * p, hp⟩ with ⟨p', s_star, h₂⟩; dsimp at h₂ 
+    rcases ore_condition r (s₂' * s_star) with ⟨p_flat, s_flat, h₃⟩; simp only [S.coe_mul] at h₃ 
     have : r₁ * r * s_flat = s₂ * p * (p' * p_flat) := by
       rw [← mul_assoc, ← h₂, ← h₁, mul_assoc, h₃]; simp only [mul_assoc]
     rw [mul'_char (r₂ * p) (r₁ * r) ⟨↑s₂ * p, hp⟩ ⟨↑s₁ * r, hr⟩ _ _ this]; clear this
@@ -237,7 +237,7 @@ protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
     rw [this]; clear this
     rcases ore_left_cancel (p * p') (r₁' * ↑s_star) s₂ (by simp [← mul_assoc, h₂]) with ⟨s₂'', h₂''⟩
     rw [← mul_assoc, mul_assoc r₂, OreLocalization.eq_of_num_factor_eq h₂'']
-    norm_cast  at hsssp⊢; rw [← OreLocalization.expand _ _ _ hsssp, ← mul_assoc]
+    norm_cast  at hsssp ⊢; rw [← OreLocalization.expand _ _ _ hsssp, ← mul_assoc]
     apply OreLocalization.expand
 #align ore_localization.mul OreLocalization.mul
 -/
@@ -260,7 +260,7 @@ theorem oreDiv_mul_char (r₁ r₂ : R) (s₁ s₂ : S) (r' : R) (s' : S) (huv :
 /-- Another characterization lemma for the multiplication on the Ore localizaion delivering
 Ore witnesses and conditions bundled in a sigma type. -/
 def oreDivMulChar' (r₁ r₂ : R) (s₁ s₂ : S) :
-    Σ'r' : R, Σ's' : S, r₂ * (s' : R) = s₁ * r' ∧ r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r₁ * r' /ₒ (s₂ * s') :=
+    Σ' r' : R, Σ' s' : S, r₂ * (s' : R) = s₁ * r' ∧ r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r₁ * r' /ₒ (s₂ * s') :=
   ⟨oreNum r₂ s₁, oreDenom r₂ s₁, ore_eq r₂ s₁, oreDiv_mul_oreDiv⟩
 #align ore_localization.ore_div_mul_char' OreLocalization.oreDivMulChar'
 
@@ -463,9 +463,9 @@ protected def localizationMap : S.LocalizationMap R[S⁻¹]
   eq_iff_exists' r₁ r₂ := by
     dsimp; constructor
     · intro h
-      rw [numerator_hom_apply, numerator_hom_apply, ore_div_eq_iff] at h
-      rcases h with ⟨u, v, h₁, h₂⟩; dsimp at h₂
-      rw [one_mul, one_mul] at h₂
+      rw [numerator_hom_apply, numerator_hom_apply, ore_div_eq_iff] at h 
+      rcases h with ⟨u, v, h₁, h₂⟩; dsimp at h₂ 
+      rw [one_mul, one_mul] at h₂ 
       subst h₂
       use u
       simpa only [mul_comm] using h₁.symm
@@ -537,7 +537,7 @@ private def add' (r₂ : R) (s₂ : S) : R[S⁻¹] → R[S⁻¹] :=
     rw [← mul_assoc, ← add_mul, ore_div_eq_iff]
     use 1; use rd; constructor
     · simp
-    · simp only [mul_one, Submonoid.coe_one, Submonoid.coe_mul] at this⊢; assoc_rw [hc, this]
+    · simp only [mul_one, Submonoid.coe_one, Submonoid.coe_mul] at this ⊢; assoc_rw [hc, this]
 
 private theorem add'_comm (r₁ r₂ : R) (s₁ s₂ : S) : add' r₁ s₁ (r₂ /ₒ s₂) = add' r₂ s₂ (r₁ /ₒ s₁) :=
   by
@@ -592,8 +592,9 @@ theorem oreDiv_add_char {r r' : R} (s s' : S) (rb : R) (sb : S) (h : (s : R) * s
 /-- Another characterization of the addition on the Ore localization, bundling up all witnesses
 and conditions into a sigma type. -/
 def oreDivAddChar' (r r' : R) (s s' : S) :
-    Σ'r'' : R,
-      Σ's'' : S, (s : R) * s'' = s' * r'' ∧ r /ₒ s + r' /ₒ s' = (r * s'' + r' * r'') /ₒ (s * s'') :=
+    Σ' r'' : R,
+      Σ' s'' : S,
+        (s : R) * s'' = s' * r'' ∧ r /ₒ s + r' /ₒ s' = (r * s'' + r' * r'') /ₒ (s * s'') :=
   ⟨oreNum s s', oreDenom s s', ore_eq s s', oreDiv_add_oreDiv⟩
 #align ore_localization.ore_div_add_char' OreLocalization.oreDivAddChar'
 
@@ -615,7 +616,7 @@ protected theorem add_assoc (x y z : R[S⁻¹]) : x + y + z = x + (y + z) :=
   repeat' rw [← add_ore_div]
   congr 1
   · rcases ore_condition (sd : R) (sa * sc) with ⟨re, se, he⟩
-    · simp_rw [← Submonoid.coe_mul] at hb hc hd
+    · simp_rw [← Submonoid.coe_mul] at hb hc hd 
       assoc_rw [Subtype.coe_eq_of_eq_mk hc]
       rw [← OreLocalization.expand, Subtype.coe_eq_of_eq_mk hd, ← mul_assoc, ←
         OreLocalization.expand, Subtype.coe_eq_of_eq_mk hb]
@@ -624,7 +625,7 @@ protected theorem add_assoc (x y z : R[S⁻¹]) : x + y + z = x + (y + z) :=
   ·
     rw [← OreLocalization.expand', ← mul_assoc, ← mul_assoc, ← OreLocalization.expand', ←
       OreLocalization.expand']
-  · simp_rw [← Submonoid.coe_mul] at ha hd
+  · simp_rw [← Submonoid.coe_mul] at ha hd 
     rw [Subtype.coe_eq_of_eq_mk hd, ← mul_assoc, ← mul_assoc, ← mul_assoc, ← OreLocalization.expand,
       ← OreLocalization.expand', Subtype.coe_eq_of_eq_mk ha, ← OreLocalization.expand]
     apply OreLocalization.expand'
@@ -706,7 +707,8 @@ theorem right_distrib (x y z : R[S⁻¹]) : (x + y) * z = x * z + y * z :=
   induction' x using OreLocalization.ind with r₁ s₁
   induction' y using OreLocalization.ind with r₂ s₂
   induction' z using OreLocalization.ind with r₃ s₃
-  rcases ore_div_add_char' r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩; rw [ha']; clear ha'; norm_cast  at ha
+  rcases ore_div_add_char' r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩; rw [ha']; clear ha';
+  norm_cast  at ha 
   rw [OreLocalization.expand' r₁ s₁ sa]
   rw [OreLocalization.expand r₂ s₂ ra (by rw [← ha] <;> apply SetLike.coe_mem)]
   rw [← Subtype.coe_eq_of_eq_mk ha]
@@ -752,7 +754,7 @@ def universalHom : R[S⁻¹] →+* T :=
       rw [add_mul, ← mul_assoc, mul_assoc (f r₁), hf, ← Units.val_mul]
       simp only [mul_one, mul_right_inv, Units.val_one]
       congr 1; rw [mul_assoc]; congr 1
-      norm_cast  at h₃; have h₃' := Subtype.coe_eq_of_eq_mk h₃
+      norm_cast  at h₃ ; have h₃' := Subtype.coe_eq_of_eq_mk h₃
       rw [← Units.val_mul, ← mul_inv_rev, ← fS.map_mul, h₃']
       have hs₂r₃ : ↑s₂ * r₃ ∈ S := by rw [← h₃]; exact SetLike.coe_mem (s₁ * s₃)
       apply (Units.inv_mul_cancel_left (fS s₂) _).symm.trans
@@ -821,15 +823,15 @@ open scoped nonZeroDivisors
 theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom : R → R[S⁻¹]) :=
   fun r₁ r₂ h =>
   by
-  rw [numerator_hom_apply, numerator_hom_apply, ore_div_eq_iff] at h
+  rw [numerator_hom_apply, numerator_hom_apply, ore_div_eq_iff] at h 
   rcases h with ⟨u, v, h₁, h₂⟩
-  simp only [S.coe_one, one_mul] at h₂
-  rwa [← h₂, mul_cancel_right_mem_nonZeroDivisors (hS (SetLike.coe_mem u)), eq_comm] at h₁
+  simp only [S.coe_one, one_mul] at h₂ 
+  rwa [← h₂, mul_cancel_right_mem_nonZeroDivisors (hS (SetLike.coe_mem u)), eq_comm] at h₁ 
 #align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_inj
 
 theorem nontrivial_of_nonZeroDivisors [Nontrivial R] (hS : S ≤ R⁰) : Nontrivial R[S⁻¹] :=
   ⟨⟨0, 1, fun h => by
-      rw [OreLocalization.one_def, OreLocalization.zero_def] at h
+      rw [OreLocalization.one_def, OreLocalization.zero_def] at h 
       apply nonZeroDivisors.coe_ne_zero 1 (numerator_hom_inj hS h).symm⟩⟩
 #align ore_localization.nontrivial_of_non_zero_divisors OreLocalization.nontrivial_of_nonZeroDivisors
 

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

@@ -232,7 +232,7 @@ protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
       exact S.mul_mem hr (SetLike.coe_mem s_flat)
     have : (⟨↑s₁ * r, hr⟩ : S) * s_flat = ⟨s₁ * s₂' * s_star * p_flat, hsssp⟩ :=
       by
-      ext; simp only [[anonymous], Submonoid.coe_mul]
+      ext; simp only [SetLike.coe_mk, Submonoid.coe_mul]
       rw [mul_assoc, h₃, ← mul_assoc, ← mul_assoc]
     rw [this]; clear this
     rcases ore_left_cancel (p * p') (r₁' * ↑s_star) s₂ (by simp [← mul_assoc, h₂]) with ⟨s₂'', h₂''⟩
@@ -388,7 +388,7 @@ def universalMulHom : R[S⁻¹] →* T
     x.liftExpand (fun r s => f r * ((fS s)⁻¹ : Units T)) fun r t s ht =>
       by
       have : (fS ⟨s * t, ht⟩ : T) = fS s * f t := by
-        simp only [← hf, [anonymous], MonoidHom.map_mul]
+        simp only [← hf, SetLike.coe_mk, MonoidHom.map_mul]
       conv_rhs =>
         rw [MonoidHom.map_mul, ← mul_one (f r), ← Units.val_one, ← mul_left_inv (fS s)]
         rw [Units.val_mul, ← mul_assoc, mul_assoc _ ↑(fS s), ← this, mul_assoc]
@@ -746,7 +746,7 @@ def universalHom : R[S⁻¹] →+* T :=
       induction' x using OreLocalization.ind with r₁ s₁
       induction' y using OreLocalization.ind with r₂ s₂
       rcases ore_div_add_char' r₁ r₂ s₁ s₂ with ⟨r₃, s₃, h₃, h₃'⟩; rw [h₃']; clear h₃'
-      simp only [universal_mul_hom_apply, [anonymous], RingHom.toMonoidHom_eq_coe,
+      simp only [universal_mul_hom_apply, RingHom.coe_monoidHom, RingHom.toMonoidHom_eq_coe,
         MonoidHom.toFun_eq_coe]
       simp only [mul_inv_rev, MonoidHom.map_mul, RingHom.map_add, RingHom.map_mul, Units.val_mul]
       rw [add_mul, ← mul_assoc, mul_assoc (f r₁), hf, ← Units.val_mul]
@@ -863,7 +863,7 @@ protected def inv : R[R⁰⁻¹] → R[R⁰⁻¹] :=
       · simp [hr]
       · by_cases ht : t = 0
         · exfalso; apply nonZeroDivisors.coe_ne_zero ⟨_, hst⟩; simp [ht, MulZeroClass.mul_zero]
-        · simp only [hr, ht, [anonymous], dif_neg, not_false_iff, or_self_iff, mul_eq_zero]
+        · simp only [hr, ht, SetLike.coe_mk, dif_neg, not_false_iff, or_self_iff, mul_eq_zero]
           apply OreLocalization.expand)
 #align ore_localization.inv OreLocalization.inv
 

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

@@ -816,7 +816,7 @@ instance : Ring R[S⁻¹] :=
   { OreLocalization.semiring, OreLocalization.hasNeg with
     add_left_neg := OreLocalization.add_left_neg }
 
-open nonZeroDivisors
+open scoped nonZeroDivisors
 
 theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom : R → R[S⁻¹]) :=
   fun r₁ r₂ h =>
@@ -837,9 +837,9 @@ end Ring
 
 section DivisionRing
 
-open nonZeroDivisors
+open scoped nonZeroDivisors
 
-open Classical
+open scoped Classical
 
 variable {R : Type _} [Ring R] [Nontrivial R] [OreSet R⁰]
 

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

@@ -52,12 +52,6 @@ namespace OreLocalization
 
 variable (R : Type _) [Monoid R] (S : Submonoid R) [OreSet S]
 
-/- warning: ore_localization.ore_eqv -> OreLocalization.oreEqv is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Monoid.{u1} R] (S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S], Setoid.{succ u1} (Prod.{u1, u1} R (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Monoid.{u1} R] (S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S], Setoid.{succ u1} (Prod.{u1, u1} R (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)))
-Case conversion may be inaccurate. Consider using '#align ore_localization.ore_eqv OreLocalization.oreEqvₓ'. -/
 /-- The setoid on `R × S` used for the Ore localization. -/
 def oreEqv : Setoid (R × S)
     where
@@ -105,12 +99,6 @@ attribute [local instance] ore_eqv
 
 variable {R S}
 
-/- warning: ore_localization.ore_div -> OreLocalization.oreDiv is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S], R -> (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (OreLocalization.{u1} R _inst_1 S _inst_2)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S], R -> (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) -> (OreLocalization.{u1} R _inst_1 S _inst_2)
-Case conversion may be inaccurate. Consider using '#align ore_localization.ore_div OreLocalization.oreDivₓ'. -/
 /-- The division in the ore localization `R[S⁻¹]`, as a fraction of an element of `R` and `S`. -/
 def oreDiv (r : R) (s : S) : R[S⁻¹] :=
   Quotient.mk' (r, s)
@@ -119,54 +107,27 @@ def oreDiv (r : R) (s : S) : R[S⁻¹] :=
 -- mathport name: «expr /ₒ »
 infixl:70 " /ₒ " => oreDiv
 
-/- warning: ore_localization.ind -> OreLocalization.ind is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ore_localization.ind OreLocalization.indₓ'. -/
 @[elab_as_elim]
 protected theorem ind {β : R[S⁻¹] → Prop} (c : ∀ (r : R) (s : S), β (r /ₒ s)) : ∀ q, β q := by
   apply Quotient.ind; rintro ⟨r, s⟩; exact c r s
 #align ore_localization.ind OreLocalization.ind
 
-/- warning: ore_localization.ore_div_eq_iff -> OreLocalization.oreDiv_eq_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ore_localization.ore_div_eq_iff OreLocalization.oreDiv_eq_iffₓ'. -/
 theorem oreDiv_eq_iff {r₁ r₂ : R} {s₁ s₂ : S} :
     r₁ /ₒ s₁ = r₂ /ₒ s₂ ↔ ∃ (u : S)(v : R), r₂ * u = r₁ * v ∧ (s₂ : R) * u = s₁ * v :=
   Quotient.eq''
 #align ore_localization.ore_div_eq_iff OreLocalization.oreDiv_eq_iff
 
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 /-- A fraction `r /ₒ s` is equal to its expansion by an arbitrary factor `t` if `s * t ∈ S`. -/
 protected theorem expand (r : R) (s : S) (t : R) (hst : (s : R) * t ∈ S) :
     r /ₒ s = r * t /ₒ ⟨s * t, hst⟩ := by apply Quotient.sound;
   refine' ⟨s, t * s, _, _⟩ <;> dsimp <;> rw [mul_assoc] <;> rfl
 #align ore_localization.expand OreLocalization.expand
 
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 /-- A fraction is equal to its expansion by an factor from s. -/
 protected theorem expand' (r : R) (s s' : S) : r /ₒ s = r * s' /ₒ (s * s') :=
   OreLocalization.expand r s s' (by norm_cast <;> apply SetLike.coe_mem)
 #align ore_localization.expand' OreLocalization.expand'
 
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 /-- Fractions which differ by a factor of the numerator can be proven equal if
 those factors expand to equal elements of `R`. -/
 protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t = r' * t) :
@@ -186,9 +147,6 @@ protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t
     
 #align ore_localization.eq_of_num_factor_eq OreLocalization.eq_of_num_factor_eq
 
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 /-- A function or predicate over `R` and `S` can be lifted to `R[S⁻¹]` if it is invariant
 under expansion on the right. -/
 def liftExpand {C : Sort _} (P : R → S → C)
@@ -203,9 +161,6 @@ def liftExpand {C : Sort _} (P : R → S → C)
     simpa [← hs₂]
 #align ore_localization.lift_expand OreLocalization.liftExpand
 
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 @[simp]
 theorem liftExpand_of {C : Sort _} {P : R → S → C}
     {hP : ∀ (r t : R) (s : S) (ht : (s : R) * t ∈ S), P r s = P (r * t) ⟨s * t, ht⟩} (r : R)
@@ -213,9 +168,6 @@ theorem liftExpand_of {C : Sort _} {P : R → S → C}
   rfl
 #align ore_localization.lift_expand_of OreLocalization.liftExpand_of
 
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 /-- A version of `lift_expand` used to simultaneously lift functions with two arguments
 in ``R[S⁻¹]`.-/
 def lift₂Expand {C : Sort _} (P : R → S → R → S → C)
@@ -232,9 +184,6 @@ def lift₂Expand {C : Sort _} (P : R → S → R → S → C)
     rw [lift_expand_of, lift_expand_of, hP r₁ t₁ s₁ ht₁ r₂ 1 s₂ (by simp)]; simp
 #align ore_localization.lift₂_expand OreLocalization.lift₂Expand
 
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 @[simp]
 theorem lift₂Expand_of {C : Sort _} {P : R → S → R → S → C}
     {hP :
@@ -296,23 +245,11 @@ protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
 instance : Mul R[S⁻¹] :=
   ⟨OreLocalization.mul⟩
 
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 theorem oreDiv_mul_oreDiv {r₁ r₂ : R} {s₁ s₂ : S} :
     r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r₁ * oreNum r₂ s₁ /ₒ (s₂ * oreDenom r₂ s₁) :=
   rfl
 #align ore_localization.ore_div_mul_ore_div OreLocalization.oreDiv_mul_oreDiv
 
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 /-- A characterization lemma for the multiplication on the Ore localization, allowing for a choice
 of Ore numerator and Ore denominator. -/
 theorem oreDiv_mul_char (r₁ r₂ : R) (s₁ s₂ : S) (r' : R) (s' : S) (huv : r₂ * (s' : R) = s₁ * r') :
@@ -320,9 +257,6 @@ theorem oreDiv_mul_char (r₁ r₂ : R) (s₁ s₂ : S) (r' : R) (s' : S) (huv :
   mul'_char r₁ r₂ s₁ s₂ s' r' huv
 #align ore_localization.ore_div_mul_char OreLocalization.oreDiv_mul_char
 
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 /-- Another characterization lemma for the multiplication on the Ore localizaion delivering
 Ore witnesses and conditions bundled in a sigma type. -/
 def oreDivMulChar' (r₁ r₂ : R) (s₁ s₂ : S) :
@@ -333,12 +267,6 @@ def oreDivMulChar' (r₁ r₂ : R) (s₁ s₂ : S) :
 instance : One R[S⁻¹] :=
   ⟨1 /ₒ 1⟩
 
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 protected theorem one_def : (1 : R[S⁻¹]) = 1 /ₒ 1 :=
   rfl
 #align ore_localization.one_def OreLocalization.one_def
@@ -346,46 +274,22 @@ protected theorem one_def : (1 : R[S⁻¹]) = 1 /ₒ 1 :=
 instance : Inhabited R[S⁻¹] :=
   ⟨1⟩
 
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 @[simp]
 protected theorem div_eq_one' {r : R} (hr : r ∈ S) : r /ₒ ⟨r, hr⟩ = 1 := by
   rw [OreLocalization.one_def, ore_div_eq_iff]; exact ⟨⟨r, hr⟩, 1, by simp, by simp⟩
 #align ore_localization.div_eq_one' OreLocalization.div_eq_one'
 
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 @[simp]
 protected theorem div_eq_one {s : S} : (s : R) /ₒ s = 1 := by
   cases s <;> apply OreLocalization.div_eq_one'
 #align ore_localization.div_eq_one OreLocalization.div_eq_one
 
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 protected theorem one_mul (x : R[S⁻¹]) : 1 * x = x :=
   by
   induction' x using OreLocalization.ind with r s
   simp [OreLocalization.one_def, ore_div_mul_char (1 : R) r (1 : S) s r 1 (by simp)]
 #align ore_localization.one_mul OreLocalization.one_mul
 
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 protected theorem mul_one (x : R[S⁻¹]) : x * 1 = x :=
   by
   induction' x using OreLocalization.ind with r s
@@ -416,64 +320,31 @@ instance : Monoid R[S⁻¹] :=
     mul_one := OreLocalization.mul_one
     mul_assoc := OreLocalization.mul_assoc }
 
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 protected theorem mul_inv (s s' : S) : (s : R) /ₒ s' * (s' /ₒ s) = 1 := by
   simp [ore_div_mul_char (s : R) s' s' s 1 1 (by simp)]
 #align ore_localization.mul_inv OreLocalization.mul_inv
 
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 @[simp]
 protected theorem mul_one_div {r : R} {s t : S} : r /ₒ s * (1 /ₒ t) = r /ₒ (t * s) := by
   simp [ore_div_mul_char r 1 s t 1 s (by simp)]
 #align ore_localization.mul_one_div OreLocalization.mul_one_div
 
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 @[simp]
 protected theorem mul_cancel {r : R} {s t : S} : r /ₒ s * (s /ₒ t) = r /ₒ t := by
   simp [ore_div_mul_char r s s t 1 1 (by simp)]
 #align ore_localization.mul_cancel OreLocalization.mul_cancel
 
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 @[simp]
 protected theorem mul_cancel' {r₁ r₂ : R} {s t : S} : r₁ /ₒ s * (s * r₂ /ₒ t) = r₁ * r₂ /ₒ t := by
   simp [ore_div_mul_char r₁ (s * r₂) s t r₂ 1 (by simp)]
 #align ore_localization.mul_cancel' OreLocalization.mul_cancel'
 
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 @[simp]
 theorem div_one_mul {p r : R} {s : S} : r /ₒ 1 * (p /ₒ s) = r * p /ₒ s :=
   by--TODO use coercion r ↦ r /ₒ 1
   simp [ore_div_mul_char r p 1 s p 1 (by simp)]
 #align ore_localization.div_one_mul OreLocalization.div_one_mul
 
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 /-- The fraction `s /ₒ 1` as a unit in `R[S⁻¹]`, where `s : S`. -/
 def numeratorUnit (s : S) : Units R[S⁻¹]
     where
@@ -483,12 +354,6 @@ def numeratorUnit (s : S) : Units R[S⁻¹]
   inv_val := OreLocalization.mul_inv 1 s
 #align ore_localization.numerator_unit OreLocalization.numeratorUnit
 
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 /-- The multiplicative homomorphism from `R` to `R[S⁻¹]`, mapping `r : R` to the
 fraction `r /ₒ 1`. -/
 def numeratorHom : R →* R[S⁻¹] where
@@ -497,22 +362,10 @@ def numeratorHom : R →* R[S⁻¹] where
   map_mul' r₁ r₂ := div_one_mul.symm
 #align ore_localization.numerator_hom OreLocalization.numeratorHom
 
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 theorem numeratorHom_apply {r : R} : numeratorHom r = r /ₒ (1 : S) :=
   rfl
 #align ore_localization.numerator_hom_apply OreLocalization.numeratorHom_apply
 
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 theorem numerator_isUnit (s : S) : IsUnit (numeratorHom (s : R) : R[S⁻¹]) :=
   ⟨numeratorUnit s, rfl⟩
 #align ore_localization.numerator_is_unit OreLocalization.numerator_isUnit
@@ -527,9 +380,6 @@ variable (hf : ∀ s : S, f s = fS s)
 
 include f fS hf
 
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 /-- The universal lift from a morphism `R →* T`, which maps elements of `S` to units of `T`,
 to a morphism `R[S⁻¹] →* T`. -/
 def universalMulHom : R[S⁻¹] →* T
@@ -559,24 +409,15 @@ def universalMulHom : R[S⁻¹] →* T
     rfl
 #align ore_localization.universal_mul_hom OreLocalization.universalMulHom
 
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 theorem universalMulHom_apply {r : R} {s : S} :
     universalMulHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
   rfl
 #align ore_localization.universal_mul_hom_apply OreLocalization.universalMulHom_apply
 
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 theorem universalMulHom_commutes {r : R} : universalMulHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_mul_hom_apply]
 #align ore_localization.universal_mul_hom_commutes OreLocalization.universalMulHom_commutes
 
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 /-- The universal morphism `universal_mul_hom` is unique. -/
 theorem universalMulHom_unique (φ : R[S⁻¹] →* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
     φ = universalMulHom f fS hf := by
@@ -594,12 +435,6 @@ section CommMonoid
 
 variable {R : Type _} [CommMonoid R] {S : Submonoid R} [OreSet S]
 
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 theorem oreDiv_mul_oreDiv_comm {r₁ r₂ : R} {s₁ s₂ : S} :
     r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r₁ * r₂ /ₒ (s₁ * s₂) := by
   rw [ore_div_mul_char r₁ r₂ s₁ s₂ r₂ s₁ (by simp [mul_comm]), mul_comm s₂]
@@ -614,12 +449,6 @@ instance : CommMonoid R[S⁻¹] :=
 
 variable (R S)
 
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 /-- The morphism `numerator_hom` is a monoid localization map in the case of commutative `R`. -/
 protected def localizationMap : S.LocalizationMap R[S⁻¹]
     where
@@ -748,17 +577,11 @@ private def add : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] := fun x =>
 instance : Add R[S⁻¹] :=
   ⟨add⟩
 
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 theorem oreDiv_add_oreDiv {r r' : R} {s s' : S} :
     r /ₒ s + r' /ₒ s' = (r * oreDenom (s : R) s' + r' * oreNum s s') /ₒ (s * oreDenom s s') :=
   rfl
 #align ore_localization.ore_div_add_ore_div OreLocalization.oreDiv_add_oreDiv
 
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 /-- A characterization of the addition on the Ore localizaion, allowing for arbitrary Ore
 numerator and Ore denominator. -/
 theorem oreDiv_add_char {r r' : R} (s s' : S) (rb : R) (sb : S) (h : (s : R) * sb = s' * rb) :
@@ -766,9 +589,6 @@ theorem oreDiv_add_char {r r' : R} (s s' : S) (rb : R) (sb : S) (h : (s : R) * s
   add''_char r s r' s' rb sb h
 #align ore_localization.ore_div_add_char OreLocalization.oreDiv_add_char
 
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 /-- Another characterization of the addition on the Ore localization, bundling up all witnesses
 and conditions into a sigma type. -/
 def oreDivAddChar' (r r' : R) (s s' : S) :
@@ -777,23 +597,11 @@ def oreDivAddChar' (r r' : R) (s s' : S) :
   ⟨oreNum s s', oreDenom s s', ore_eq s s', oreDiv_add_oreDiv⟩
 #align ore_localization.ore_div_add_char' OreLocalization.oreDivAddChar'
 
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 @[simp]
 theorem add_oreDiv {r r' : R} {s : S} : r /ₒ s + r' /ₒ s = (r + r') /ₒ s := by
   simp [ore_div_add_char s s 1 1 (by simp)]
 #align ore_localization.add_ore_div OreLocalization.add_oreDiv
 
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 protected theorem add_assoc (x y z : R[S⁻¹]) : x + y + z = x + (y + z) :=
   by
   induction' x using OreLocalization.ind with r₁ s₁
@@ -828,45 +636,21 @@ private def zero : R[S⁻¹] :=
 instance : Zero R[S⁻¹] :=
   ⟨zero⟩
 
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 protected theorem zero_def : (0 : R[S⁻¹]) = 0 /ₒ 1 :=
   rfl
 #align ore_localization.zero_def OreLocalization.zero_def
 
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 @[simp]
 theorem zero_div_eq_zero (s : S) : 0 /ₒ s = 0 := by rw [OreLocalization.zero_def, ore_div_eq_iff];
   exact ⟨s, 1, by simp⟩
 #align ore_localization.zero_div_eq_zero OreLocalization.zero_div_eq_zero
 
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 protected theorem zero_add (x : R[S⁻¹]) : 0 + x = x :=
   by
   induction x using OreLocalization.ind
   rw [← zero_div_eq_zero, add_ore_div]; simp
 #align ore_localization.zero_add OreLocalization.zero_add
 
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-Case conversion may be inaccurate. Consider using '#align ore_localization.add_comm OreLocalization.add_commₓ'. -/
 protected theorem add_comm (x y : R[S⁻¹]) : x + y = y + x :=
   by
   induction x using OreLocalization.ind
@@ -882,36 +666,18 @@ instance : AddCommMonoid R[S⁻¹] :=
     zero_add := OreLocalization.zero_add
     add_zero := fun x => by rw [OreLocalization.add_comm, OreLocalization.zero_add] }
 
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 protected theorem zero_mul (x : R[S⁻¹]) : 0 * x = 0 :=
   by
   induction' x using OreLocalization.ind with r s
   rw [OreLocalization.zero_def, ore_div_mul_char 0 r 1 s r 1 (by simp)]; simp
 #align ore_localization.zero_mul OreLocalization.zero_mul
 
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-Case conversion may be inaccurate. Consider using '#align ore_localization.mul_zero OreLocalization.mul_zeroₓ'. -/
 protected theorem mul_zero (x : R[S⁻¹]) : x * 0 = 0 :=
   by
   induction' x using OreLocalization.ind with r s
   rw [OreLocalization.zero_def, ore_div_mul_char r 0 s 1 0 1 (by simp)]; simp
 #align ore_localization.mul_zero OreLocalization.mul_zero
 
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-Case conversion may be inaccurate. Consider using '#align ore_localization.left_distrib OreLocalization.left_distribₓ'. -/
 protected theorem left_distrib (x y z : R[S⁻¹]) : x * (y + z) = x * y + x * z :=
   by
   induction' x using OreLocalization.ind with r₁ s₁
@@ -935,12 +701,6 @@ protected theorem left_distrib (x y z : R[S⁻¹]) : x * (y + z) = x * y + x * z
   rw [OreLocalization.mul_cancel']; simp only [mul_one, Submonoid.coe_mul, mul_add, ← mul_assoc]
 #align ore_localization.left_distrib OreLocalization.left_distrib
 
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-Case conversion may be inaccurate. Consider using '#align ore_localization.right_distrib OreLocalization.right_distribₓ'. -/
 theorem right_distrib (x y z : R[S⁻¹]) : (x + y) * z = x * z + y * z :=
   by
   induction' x using OreLocalization.ind with r₁ s₁
@@ -971,9 +731,6 @@ variable (hf : ∀ s : S, f s = fS s)
 
 include f fS hf
 
-/- warning: ore_localization.universal_hom -> OreLocalization.universalHom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom OreLocalization.universalHomₓ'. -/
 /-- The universal lift from a ring homomorphism `f : R →+* T`, which maps elements in `S` to
 units of `T`, to a ring homomorphism `R[S⁻¹] →+* T`. This extends the construction on
 monoids. -/
@@ -1015,24 +772,15 @@ def universalHom : R[S⁻¹] →+* T :=
       rw [one_mul, ← h₃', Units.mul_inv, mul_one] }
 #align ore_localization.universal_hom OreLocalization.universalHom
 
-/- warning: ore_localization.universal_hom_apply -> OreLocalization.universalHom_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_apply OreLocalization.universalHom_applyₓ'. -/
 theorem universalHom_apply {r : R} {s : S} :
     universalHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
   rfl
 #align ore_localization.universal_hom_apply OreLocalization.universalHom_apply
 
-/- warning: ore_localization.universal_hom_commutes -> OreLocalization.universalHom_commutes is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_commutes OreLocalization.universalHom_commutesₓ'. -/
 theorem universalHom_commutes {r : R} : universalHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_hom_apply]
 #align ore_localization.universal_hom_commutes OreLocalization.universalHom_commutes
 
-/- warning: ore_localization.universal_hom_unique -> OreLocalization.universalHom_unique is a dubious translation:
-<too large>
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 theorem universalHom_unique (φ : R[S⁻¹] →+* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
     φ = universalHom f fS hf :=
   RingHom.coe_monoidHom_injective <| universalMulHom_unique (RingHom.toMonoidHom f) fS hf (↑φ) huniv
@@ -1046,12 +794,6 @@ section Ring
 
 variable {R : Type _} [Ring R] {S : Submonoid R} [OreSet S]
 
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 /-- Negation on the Ore localization is defined via negation on the numerator. -/
 protected def neg : R[S⁻¹] → R[S⁻¹] :=
   liftExpand (fun (r : R) (s : S) => -r /ₒ s) fun r t s ht => by
@@ -1061,23 +803,11 @@ protected def neg : R[S⁻¹] → R[S⁻¹] :=
 instance : Neg R[S⁻¹] :=
   ⟨OreLocalization.neg⟩
 
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 @[simp]
 protected theorem neg_def (r : R) (s : S) : -(r /ₒ s) = -r /ₒ s :=
   rfl
 #align ore_localization.neg_def OreLocalization.neg_def
 
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 protected theorem add_left_neg (x : R[S⁻¹]) : -x + x = 0 := by
   induction' x using OreLocalization.ind with r s <;> simp
 #align ore_localization.add_left_neg OreLocalization.add_left_neg
@@ -1088,12 +818,6 @@ instance : Ring R[S⁻¹] :=
 
 open nonZeroDivisors
 
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(MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
-Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_injₓ'. -/
 theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom : R → R[S⁻¹]) :=
   fun r₁ r₂ h =>
   by
@@ -1103,12 +827,6 @@ theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom :
   rwa [← h₂, mul_cancel_right_mem_nonZeroDivisors (hS (SetLike.coe_mem u)), eq_comm] at h₁
 #align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_inj
 
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-Case conversion may be inaccurate. Consider using '#align ore_localization.nontrivial_of_non_zero_divisors OreLocalization.nontrivial_of_nonZeroDivisorsₓ'. -/
 theorem nontrivial_of_nonZeroDivisors [Nontrivial R] (hS : S ≤ R⁰) : Nontrivial R[S⁻¹] :=
   ⟨⟨0, 1, fun h => by
       rw [OreLocalization.one_def, OreLocalization.zero_def] at h
@@ -1132,12 +850,6 @@ variable [NoZeroDivisors R]
 
 noncomputable section
 
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-Case conversion may be inaccurate. Consider using '#align ore_localization.inv OreLocalization.invₓ'. -/
 /-- The inversion of Ore fractions for a ring without zero divisors, satisying `0⁻¹ = 0` and
 `(r /ₒ r')⁻¹ = r' /ₒ r` for `r ≠ 0`. -/
 protected def inv : R[R⁰⁻¹] → R[R⁰⁻¹] :=
@@ -1158,9 +870,6 @@ protected def inv : R[R⁰⁻¹] → R[R⁰⁻¹] :=
 instance : Inv R[R⁰⁻¹] :=
   ⟨OreLocalization.inv⟩
 
-/- warning: ore_localization.inv_def -> OreLocalization.inv_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ore_localization.inv_def OreLocalization.inv_defₓ'. -/
 protected theorem inv_def {r : R} {s : R⁰} :
     (r /ₒ s)⁻¹ =
       if hr : r = (0 : R) then (0 : R[R⁰⁻¹])
@@ -1168,12 +877,6 @@ protected theorem inv_def {r : R} {s : R⁰} :
   rfl
 #align ore_localization.inv_def OreLocalization.inv_def
 
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-Case conversion may be inaccurate. Consider using '#align ore_localization.mul_inv_cancel OreLocalization.mul_inv_cancelₓ'. -/
 protected theorem mul_inv_cancel (x : R[R⁰⁻¹]) (h : x ≠ 0) : x * x⁻¹ = 1 :=
   by
   induction' x using OreLocalization.ind with r s
@@ -1183,12 +886,6 @@ protected theorem mul_inv_cancel (x : R[R⁰⁻¹]) (h : x ≠ 0) : x * x⁻¹ =
   · simp [hr]; apply OreLocalization.div_eq_one'
 #align ore_localization.mul_inv_cancel OreLocalization.mul_inv_cancel
 
-/- warning: ore_localization.inv_zero -> OreLocalization.inv_zero is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))] [_inst_4 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))], Eq.{succ u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (Inv.inv.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.hasInv.{u1} R _inst_1 _inst_2 _inst_3 _inst_4) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) 0 (OfNat.mk.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) 0 (Zero.zero.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.hasZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3))))) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) 0 (OfNat.mk.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) 0 (Zero.zero.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.hasZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3))))
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-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))], Eq.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (Inv.inv.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.inv'.{u1} R _inst_1 _inst_2 _inst_3 _inst_4) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) 0 (Zero.toOfNat0.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.instZeroOreLocalizationToMonoidToMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3)))) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) 0 (Zero.toOfNat0.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.instZeroOreLocalizationToMonoidToMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3)))
-Case conversion may be inaccurate. Consider using '#align ore_localization.inv_zero OreLocalization.inv_zeroₓ'. -/
 protected theorem inv_zero : (0 : R[R⁰⁻¹])⁻¹ = 0 := by
   rw [OreLocalization.zero_def, OreLocalization.inv_def]; simp
 #align ore_localization.inv_zero OreLocalization.inv_zero

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

@@ -64,31 +64,19 @@ def oreEqv : Setoid (R × S)
   R rs rs' := ∃ (u : S)(v : R), rs'.1 * u = rs.1 * v ∧ (rs'.2 : R) * u = rs.2 * v
   iseqv := by
     refine' ⟨_, _, _⟩
-    · rintro ⟨r, s⟩
-      use 1
-      use 1
-      simp [Submonoid.one_mem]
+    · rintro ⟨r, s⟩; use 1; use 1; simp [Submonoid.one_mem]
     · rintro ⟨r, s⟩ ⟨r', s'⟩ ⟨u, v, hru, hsu⟩
       rcases ore_condition (s : R) s' with ⟨r₂, s₂, h₁⟩
       rcases ore_condition r₂ u with ⟨r₃, s₃, h₂⟩
-      have : (s : R) * ((v : R) * r₃) = (s : R) * (s₂ * s₃) :=
-        by
-        assoc_rw [h₁, h₂, hsu]
-        symm
+      have : (s : R) * ((v : R) * r₃) = (s : R) * (s₂ * s₃) := by assoc_rw [h₁, h₂, hsu]; symm;
         apply mul_assoc
       rcases ore_left_cancel (v * r₃) (s₂ * s₃) s this with ⟨w, hw⟩
-      use s₂ * s₃ * w
-      use u * r₃ * w
-      constructor <;> simp only [Submonoid.coe_mul]
-      · assoc_rw [hru, ← hw]
-        simp [mul_assoc]
-      · assoc_rw [hsu, ← hw]
-        simp [mul_assoc]
+      use s₂ * s₃ * w; use u * r₃ * w; constructor <;> simp only [Submonoid.coe_mul]
+      · assoc_rw [hru, ← hw]; simp [mul_assoc]
+      · assoc_rw [hsu, ← hw]; simp [mul_assoc]
     · rintro ⟨r₁, s₁⟩ ⟨r₂, s₂⟩ ⟨r₃, s₃⟩ ⟨u, v, hur₁, hs₁u⟩ ⟨u', v', hur₂, hs₂u⟩
       rcases ore_condition v' u with ⟨r', s', h⟩
-      use u' * s'
-      use v * r'
-      constructor <;> simp only [Submonoid.coe_mul]
+      use u' * s'; use v * r'; constructor <;> simp only [Submonoid.coe_mul]
       · assoc_rw [hur₂, h, hur₁, mul_assoc]
       · assoc_rw [hs₂u, h, hs₁u, mul_assoc]
 #align ore_localization.ore_eqv OreLocalization.oreEqv
@@ -138,11 +126,8 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {β : (OreLocalization.{u1} R _inst_1 S _inst_2) -> Prop}, (forall (r : R) (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), β (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r s)) -> (forall (q : OreLocalization.{u1} R _inst_1 S _inst_2), β q)
 Case conversion may be inaccurate. Consider using '#align ore_localization.ind OreLocalization.indₓ'. -/
 @[elab_as_elim]
-protected theorem ind {β : R[S⁻¹] → Prop} (c : ∀ (r : R) (s : S), β (r /ₒ s)) : ∀ q, β q :=
-  by
-  apply Quotient.ind
-  rintro ⟨r, s⟩
-  exact c r s
+protected theorem ind {β : R[S⁻¹] → Prop} (c : ∀ (r : R) (s : S), β (r /ₒ s)) : ∀ q, β q := by
+  apply Quotient.ind; rintro ⟨r, s⟩; exact c r s
 #align ore_localization.ind OreLocalization.ind
 
 /- warning: ore_localization.ore_div_eq_iff -> OreLocalization.oreDiv_eq_iff is a dubious translation:
@@ -161,8 +146,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ore_localization.expand OreLocalization.expandₓ'. -/
 /-- A fraction `r /ₒ s` is equal to its expansion by an arbitrary factor `t` if `s * t ∈ S`. -/
 protected theorem expand (r : R) (s : S) (t : R) (hst : (s : R) * t ∈ S) :
-    r /ₒ s = r * t /ₒ ⟨s * t, hst⟩ := by
-  apply Quotient.sound
+    r /ₒ s = r * t /ₒ ⟨s * t, hst⟩ := by apply Quotient.sound;
   refine' ⟨s, t * s, _, _⟩ <;> dsimp <;> rw [mul_assoc] <;> rfl
 #align ore_localization.expand OreLocalization.expand
 
@@ -211,23 +195,11 @@ def liftExpand {C : Sort _} (P : R → S → C)
     (hP : ∀ (r t : R) (s : S) (ht : (s : R) * t ∈ S), P r s = P (r * t) ⟨s * t, ht⟩) : R[S⁻¹] → C :=
   Quotient.lift (fun p : R × S => P p.1 p.2) fun p q pq =>
     by
-    cases' p with r₁ s₁
-    cases' q with r₂ s₂
-    rcases pq with ⟨u, v, hr₂, hs₂⟩
+    cases' p with r₁ s₁; cases' q with r₂ s₂; rcases pq with ⟨u, v, hr₂, hs₂⟩
     dsimp at *
-    have s₁vS : (s₁ : R) * v ∈ S := by
-      rw [← hs₂, ← S.coe_mul]
-      exact SetLike.coe_mem (s₂ * u)
-    replace hs₂ : s₂ * u = ⟨(s₁ : R) * v, s₁vS⟩
-    · ext
-      simp [hs₂]
-    rw [hP r₁ v s₁ s₁vS,
-      hP r₂ u s₂
-        (by
-          norm_cast
-          rw [hs₂]
-          assumption),
-      hr₂]
+    have s₁vS : (s₁ : R) * v ∈ S := by rw [← hs₂, ← S.coe_mul]; exact SetLike.coe_mem (s₂ * u)
+    replace hs₂ : s₂ * u = ⟨(s₁ : R) * v, s₁vS⟩; · ext; simp [hs₂]
+    rw [hP r₁ v s₁ s₁vS, hP r₂ u s₂ (by norm_cast; rw [hs₂]; assumption), hr₂]
     simpa [← hs₂]
 #align ore_localization.lift_expand OreLocalization.liftExpand
 
@@ -291,44 +263,32 @@ private theorem mul'_char (r₁ r₂ : R) (s₁ s₂ : S) (u : S) (v : R) (huv :
   rcases ore_left_cancel _ _ _ this with ⟨s₄, hs₄⟩
   symm; rw [ore_div_eq_iff]
   use s₃ * s₄; use r₃ * s₄; simp only [Submonoid.coe_mul]; constructor
-  · assoc_rw [← hs₄]
-    simp only [mul_assoc]
-  · assoc_rw [h₃]
-    simp only [mul_assoc]
+  · assoc_rw [← hs₄]; simp only [mul_assoc]
+  · assoc_rw [h₃]; simp only [mul_assoc]
 
 #print OreLocalization.mul /-
 /-- The multiplication on the Ore localization of monoids. -/
 protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
   lift₂Expand mul' fun r₂ p s₂ hp r₁ r s₁ hr =>
     by
-    have h₁ := ore_eq r₁ s₂
-    set r₁' := ore_num r₁ s₂
-    set s₂' := ore_denom r₁ s₂
-    rcases ore_condition (↑s₂ * r₁') ⟨s₂ * p, hp⟩ with ⟨p', s_star, h₂⟩
-    dsimp at h₂
-    rcases ore_condition r (s₂' * s_star) with ⟨p_flat, s_flat, h₃⟩
-    simp only [S.coe_mul] at h₃
-    have : r₁ * r * s_flat = s₂ * p * (p' * p_flat) :=
-      by
-      rw [← mul_assoc, ← h₂, ← h₁, mul_assoc, h₃]
-      simp only [mul_assoc]
-    rw [mul'_char (r₂ * p) (r₁ * r) ⟨↑s₂ * p, hp⟩ ⟨↑s₁ * r, hr⟩ _ _ this]
-    clear this
+    have h₁ := ore_eq r₁ s₂; set r₁' := ore_num r₁ s₂; set s₂' := ore_denom r₁ s₂
+    rcases ore_condition (↑s₂ * r₁') ⟨s₂ * p, hp⟩ with ⟨p', s_star, h₂⟩; dsimp at h₂
+    rcases ore_condition r (s₂' * s_star) with ⟨p_flat, s_flat, h₃⟩; simp only [S.coe_mul] at h₃
+    have : r₁ * r * s_flat = s₂ * p * (p' * p_flat) := by
+      rw [← mul_assoc, ← h₂, ← h₁, mul_assoc, h₃]; simp only [mul_assoc]
+    rw [mul'_char (r₂ * p) (r₁ * r) ⟨↑s₂ * p, hp⟩ ⟨↑s₁ * r, hr⟩ _ _ this]; clear this
     have hsssp : ↑s₁ * ↑s₂' * ↑s_star * p_flat ∈ S :=
       by
       rw [mul_assoc, mul_assoc, ← mul_assoc ↑s₂', ← h₃, ← mul_assoc]
       exact S.mul_mem hr (SetLike.coe_mem s_flat)
     have : (⟨↑s₁ * r, hr⟩ : S) * s_flat = ⟨s₁ * s₂' * s_star * p_flat, hsssp⟩ :=
       by
-      ext
-      simp only [[anonymous], Submonoid.coe_mul]
+      ext; simp only [[anonymous], Submonoid.coe_mul]
       rw [mul_assoc, h₃, ← mul_assoc, ← mul_assoc]
-    rw [this]
-    clear this
+    rw [this]; clear this
     rcases ore_left_cancel (p * p') (r₁' * ↑s_star) s₂ (by simp [← mul_assoc, h₂]) with ⟨s₂'', h₂''⟩
     rw [← mul_assoc, mul_assoc r₂, OreLocalization.eq_of_num_factor_eq h₂'']
-    norm_cast  at hsssp⊢
-    rw [← OreLocalization.expand _ _ _ hsssp, ← mul_assoc]
+    norm_cast  at hsssp⊢; rw [← OreLocalization.expand _ _ _ hsssp, ← mul_assoc]
     apply OreLocalization.expand
 #align ore_localization.mul OreLocalization.mul
 -/
@@ -393,10 +353,8 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R} (hr : Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) r S), Eq.{succ u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (Subtype.mk.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S) r hr)) (OfNat.ofNat.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) 1 (One.toOfNat1.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instOneOreLocalization.{u1} R _inst_1 S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align ore_localization.div_eq_one' OreLocalization.div_eq_one'ₓ'. -/
 @[simp]
-protected theorem div_eq_one' {r : R} (hr : r ∈ S) : r /ₒ ⟨r, hr⟩ = 1 :=
-  by
-  rw [OreLocalization.one_def, ore_div_eq_iff]
-  exact ⟨⟨r, hr⟩, 1, by simp, by simp⟩
+protected theorem div_eq_one' {r : R} (hr : r ∈ S) : r /ₒ ⟨r, hr⟩ = 1 := by
+  rw [OreLocalization.one_def, ore_div_eq_iff]; exact ⟨⟨r, hr⟩, 1, by simp, by simp⟩
 #align ore_localization.div_eq_one' OreLocalization.div_eq_one'
 
 /- warning: ore_localization.div_eq_one -> OreLocalization.div_eq_one is a dubious translation:
@@ -444,9 +402,7 @@ protected theorem mul_assoc (x y z : R[S⁻¹]) : x * y * z = x * (y * z) :=
   rcases ore_div_mul_char' r₂ r₃ s₂ s₃ with ⟨rb, sb, hb, hb'⟩; rw [hb']; clear hb'
   rcases ore_condition rb sa with ⟨rc, sc, hc⟩
   rw [ore_div_mul_char (r₁ * ra) r₃ (s₂ * sa) s₃ rc (sb * sc)
-      (by
-        simp only [Submonoid.coe_mul]
-        assoc_rw [hb, hc])]
+      (by simp only [Submonoid.coe_mul]; assoc_rw [hb, hc])]
   rw [mul_assoc, ← mul_assoc s₃]
   symm; apply ore_div_mul_char
   assoc_rw [hc, ← ha]; apply mul_assoc
@@ -679,8 +635,7 @@ protected def localizationMap : S.LocalizationMap R[S⁻¹]
     dsimp; constructor
     · intro h
       rw [numerator_hom_apply, numerator_hom_apply, ore_div_eq_iff] at h
-      rcases h with ⟨u, v, h₁, h₂⟩
-      dsimp at h₂
+      rcases h with ⟨u, v, h₁, h₂⟩; dsimp at h₂
       rw [one_mul, one_mul] at h₂
       subst h₂
       use u
@@ -713,13 +668,10 @@ private theorem add''_char (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) (rb : R)
   by
   simp only [add'']
   have ha := ore_eq (s₁ : R) s₂
-  set! ra := ore_num (s₁ : R) s₂ with h
-  rw [← h] at *
-  clear h
+  set! ra := ore_num (s₁ : R) s₂ with h; rw [← h] at *; clear h
   -- r tilde
-  set! sa := ore_denom (s₁ : R) s₂ with h
-  rw [← h] at *
-  clear h
+  set! sa := ore_denom (s₁ : R) s₂ with h;
+  rw [← h] at *; clear h
   -- s tilde
   rcases ore_condition (sa : R) sb with ⟨rc, sc, hc⟩
   -- s*, r*
@@ -727,16 +679,12 @@ private theorem add''_char (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) (rb : R)
     rw [← mul_assoc, ← hb, mul_assoc, ← hc, ← mul_assoc, ← mul_assoc, ha]
   rcases ore_left_cancel _ _ s₂ this with ⟨sd, hd⟩
   -- s#
-  symm
+  symm;
   rw [ore_div_eq_iff]
-  use sc * sd
-  use rc * sd
+  use sc * sd; use rc * sd
   constructor <;> simp only [Submonoid.coe_mul]
-  · noncomm_ring
-    assoc_rw [hd, hc]
-    noncomm_ring
-  · assoc_rw [hc]
-    noncomm_ring
+  · noncomm_ring; assoc_rw [hd, hc]; noncomm_ring
+  · assoc_rw [hc]; noncomm_ring
 
 attribute [local instance] OreLocalization.oreEqv
 
@@ -751,44 +699,30 @@ private def add' (r₂ : R) (s₂ : S) : R[S⁻¹] → R[S⁻¹] :=
     --s~~, r~~
     rcases ore_condition rb sc with ⟨rd, sd, hd⟩
     -- s#, r#
-    dsimp at *
+    dsimp at *;
     rw [add''_char _ _ _ _ rc sc hc]
-    have : ↑s₁ * ↑(sb * sd) = ↑s₂ * (rc * rd) :=
-      by
-      simp only [Submonoid.coe_mul]
-      assoc_rw [hb', hd, hc]
-      noncomm_ring
+    have : ↑s₁ * ↑(sb * sd) = ↑s₂ * (rc * rd) := by simp only [Submonoid.coe_mul];
+      assoc_rw [hb', hd, hc]; noncomm_ring
     rw [add''_char _ _ _ _ (rc * rd : R) (sb * sd : S) this]
-    simp only [Submonoid.coe_mul]
-    assoc_rw [hb, hd]
+    simp only [Submonoid.coe_mul]; assoc_rw [hb, hd]
     rw [← mul_assoc, ← add_mul, ore_div_eq_iff]
-    use 1
-    use rd
-    constructor
+    use 1; use rd; constructor
     · simp
-    · simp only [mul_one, Submonoid.coe_one, Submonoid.coe_mul] at this⊢
-      assoc_rw [hc, this]
+    · simp only [mul_one, Submonoid.coe_one, Submonoid.coe_mul] at this⊢; assoc_rw [hc, this]
 
 private theorem add'_comm (r₁ r₂ : R) (s₁ s₂ : S) : add' r₁ s₁ (r₂ /ₒ s₂) = add' r₂ s₂ (r₁ /ₒ s₁) :=
   by
   simp only [add', ore_div, add'', Quotient.lift_mk, Quotient.eq']
-  have hb := ore_eq (↑s₂) s₁
-  set rb := ore_num (↑s₂) s₁ with h
+  have hb := ore_eq (↑s₂) s₁; set rb := ore_num (↑s₂) s₁ with h
   -- r~~
-  rw [← h]
-  clear h
-  set sb := ore_denom (↑s₂) s₁ with h
-  rw [← h]
-  clear h
+  rw [← h];
+  clear h; set sb := ore_denom (↑s₂) s₁ with h; rw [← h]; clear h
   -- s~~
-  have ha := ore_eq (↑s₁) s₂
+  have ha := ore_eq (↑s₁) s₂;
   set ra := ore_num (↑s₁) s₂ with h
   -- r~
-  rw [← h]
-  clear h
-  set sa := ore_denom (↑s₁) s₂ with h
-  rw [← h]
-  clear h
+  rw [← h];
+  clear h; set sa := ore_denom (↑s₁) s₂ with h; rw [← h]; clear h
   -- s~
   rcases ore_condition ra sb with ⟨rc, sc, hc⟩
   -- r#, s#
@@ -796,15 +730,11 @@ private theorem add'_comm (r₁ r₂ : R) (s₁ s₂ : S) : add' r₁ s₁ (r₂
     rw [← mul_assoc, ← hb, mul_assoc, ← hc, ← mul_assoc, ← ha, mul_assoc]
   rcases ore_left_cancel _ _ s₁ this with ⟨sd, hd⟩
   -- s+
-  use sc * sd
+  use sc * sd;
   use rc * sd
-  dsimp
-  constructor
-  · rw [add_mul, add_mul, add_comm]
-    assoc_rw [← hd, hc]
-    noncomm_ring
-  · rw [mul_assoc, ← mul_assoc ↑sa, ← hd, hb]
-    noncomm_ring
+  dsimp; constructor
+  · rw [add_mul, add_mul, add_comm]; assoc_rw [← hd, hc]; noncomm_ring
+  · rw [mul_assoc, ← mul_assoc ↑sa, ← hd, hb]; noncomm_ring
 
 /-- The addition on the Ore localization. -/
 private def add : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] := fun x =>
@@ -915,9 +845,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)), Eq.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.oreDiv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) s) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) 0 (Zero.toOfNat0.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instZeroOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align ore_localization.zero_div_eq_zero OreLocalization.zero_div_eq_zeroₓ'. -/
 @[simp]
-theorem zero_div_eq_zero (s : S) : 0 /ₒ s = 0 :=
-  by
-  rw [OreLocalization.zero_def, ore_div_eq_iff]
+theorem zero_div_eq_zero (s : S) : 0 /ₒ s = 0 := by rw [OreLocalization.zero_def, ore_div_eq_iff];
   exact ⟨s, 1, by simp⟩
 #align ore_localization.zero_div_eq_zero OreLocalization.zero_div_eq_zero
 
@@ -989,23 +917,14 @@ protected theorem left_distrib (x y z : R[S⁻¹]) : x * (y + z) = x * y + x * z
   induction' x using OreLocalization.ind with r₁ s₁
   induction' y using OreLocalization.ind with r₂ s₂
   induction' z using OreLocalization.ind with r₃ s₃
-  rcases ore_div_add_char' r₂ r₃ s₂ s₃ with ⟨ra, sa, ha, q⟩
-  rw [q]
-  clear q
+  rcases ore_div_add_char' r₂ r₃ s₂ s₃ with ⟨ra, sa, ha, q⟩; rw [q]; clear q
   rw [OreLocalization.expand' r₂ s₂ sa]
-  rcases ore_div_mul_char' r₁ (r₂ * sa) s₁ (s₂ * sa) with ⟨rb, sb, hb, q⟩
-  rw [q]
-  clear q
-  have hs₃rasb : ↑s₃ * (ra * sb) ∈ S :=
-    by
-    rw [← mul_assoc, ← ha]
-    norm_cast
-    apply SetLike.coe_mem
+  rcases ore_div_mul_char' r₁ (r₂ * sa) s₁ (s₂ * sa) with ⟨rb, sb, hb, q⟩; rw [q]; clear q
+  have hs₃rasb : ↑s₃ * (ra * sb) ∈ S := by rw [← mul_assoc, ← ha]; norm_cast; apply SetLike.coe_mem
   rw [OreLocalization.expand _ _ _ hs₃rasb]
   have ha' : ↑(s₂ * sa * sb) = ↑s₃ * (ra * sb) := by simp [ha, ← mul_assoc]
   rw [← Subtype.coe_eq_of_eq_mk ha']
-  rcases ore_div_mul_char' r₁ (r₃ * (ra * sb)) s₁ (s₂ * sa * sb) with ⟨rc, sc, hc, hc'⟩
-  rw [hc']
+  rcases ore_div_mul_char' r₁ (r₃ * (ra * sb)) s₁ (s₂ * sa * sb) with ⟨rc, sc, hc, hc'⟩; rw [hc']
   rw [ore_div_add_char (s₂ * sa * sb) (s₂ * sa * sb * sc) 1 sc (by simp)]
   rw [OreLocalization.expand' (r₂ * ↑sa + r₃ * ra) (s₂ * sa) (sb * sc)]
   conv_lhs =>
@@ -1013,8 +932,7 @@ protected theorem left_distrib (x y z : R[S⁻¹]) : x * (y + z) = x * y + x * z
     skip
     congr
     rw [add_mul, S.coe_mul, ← mul_assoc, hb, ← mul_assoc, mul_assoc r₃, hc, mul_assoc, ← mul_add]
-  rw [OreLocalization.mul_cancel']
-  simp only [mul_one, Submonoid.coe_mul, mul_add, ← mul_assoc]
+  rw [OreLocalization.mul_cancel']; simp only [mul_one, Submonoid.coe_mul, mul_add, ← mul_assoc]
 #align ore_localization.left_distrib OreLocalization.left_distrib
 
 /- warning: ore_localization.right_distrib -> OreLocalization.right_distrib is a dubious translation:
@@ -1070,23 +988,16 @@ def universalHom : R[S⁻¹] →+* T :=
     map_add' := fun x y => by
       induction' x using OreLocalization.ind with r₁ s₁
       induction' y using OreLocalization.ind with r₂ s₂
-      rcases ore_div_add_char' r₁ r₂ s₁ s₂ with ⟨r₃, s₃, h₃, h₃'⟩
-      rw [h₃']
-      clear h₃'
+      rcases ore_div_add_char' r₁ r₂ s₁ s₂ with ⟨r₃, s₃, h₃, h₃'⟩; rw [h₃']; clear h₃'
       simp only [universal_mul_hom_apply, [anonymous], RingHom.toMonoidHom_eq_coe,
         MonoidHom.toFun_eq_coe]
       simp only [mul_inv_rev, MonoidHom.map_mul, RingHom.map_add, RingHom.map_mul, Units.val_mul]
       rw [add_mul, ← mul_assoc, mul_assoc (f r₁), hf, ← Units.val_mul]
       simp only [mul_one, mul_right_inv, Units.val_one]
-      congr 1
-      rw [mul_assoc]
-      congr 1
-      norm_cast  at h₃
-      have h₃' := Subtype.coe_eq_of_eq_mk h₃
+      congr 1; rw [mul_assoc]; congr 1
+      norm_cast  at h₃; have h₃' := Subtype.coe_eq_of_eq_mk h₃
       rw [← Units.val_mul, ← mul_inv_rev, ← fS.map_mul, h₃']
-      have hs₂r₃ : ↑s₂ * r₃ ∈ S := by
-        rw [← h₃]
-        exact SetLike.coe_mem (s₁ * s₃)
+      have hs₂r₃ : ↑s₂ * r₃ ∈ S := by rw [← h₃]; exact SetLike.coe_mem (s₁ * s₃)
       apply (Units.inv_mul_cancel_left (fS s₂) _).symm.trans
       conv_lhs =>
         congr
@@ -1239,9 +1150,7 @@ protected def inv : R[R⁰⁻¹] → R[R⁰⁻¹] :=
       by_cases hr : r = 0
       · simp [hr]
       · by_cases ht : t = 0
-        · exfalso
-          apply nonZeroDivisors.coe_ne_zero ⟨_, hst⟩
-          simp [ht, MulZeroClass.mul_zero]
+        · exfalso; apply nonZeroDivisors.coe_ne_zero ⟨_, hst⟩; simp [ht, MulZeroClass.mul_zero]
         · simp only [hr, ht, [anonymous], dif_neg, not_false_iff, or_self_iff, mul_eq_zero]
           apply OreLocalization.expand)
 #align ore_localization.inv OreLocalization.inv
@@ -1270,11 +1179,8 @@ protected theorem mul_inv_cancel (x : R[R⁰⁻¹]) (h : x ≠ 0) : x * x⁻¹ =
   induction' x using OreLocalization.ind with r s
   rw [OreLocalization.inv_def, OreLocalization.one_def]
   by_cases hr : r = 0
-  · exfalso
-    apply h
-    simp [hr]
-  · simp [hr]
-    apply OreLocalization.div_eq_one'
+  · exfalso; apply h; simp [hr]
+  · simp [hr]; apply OreLocalization.div_eq_one'
 #align ore_localization.mul_inv_cancel OreLocalization.mul_inv_cancel
 
 /- warning: ore_localization.inv_zero -> OreLocalization.inv_zero is a dubious translation:
@@ -1283,10 +1189,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))], Eq.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (Inv.inv.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.inv'.{u1} R _inst_1 _inst_2 _inst_3 _inst_4) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) 0 (Zero.toOfNat0.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.instZeroOreLocalizationToMonoidToMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3)))) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) 0 (Zero.toOfNat0.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.instZeroOreLocalizationToMonoidToMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align ore_localization.inv_zero OreLocalization.inv_zeroₓ'. -/
-protected theorem inv_zero : (0 : R[R⁰⁻¹])⁻¹ = 0 :=
-  by
-  rw [OreLocalization.zero_def, OreLocalization.inv_def]
-  simp
+protected theorem inv_zero : (0 : R[R⁰⁻¹])⁻¹ = 0 := by
+  rw [OreLocalization.zero_def, OreLocalization.inv_def]; simp
 #align ore_localization.inv_zero OreLocalization.inv_zero
 
 instance : DivisionRing R[R⁰⁻¹] :=

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

@@ -146,10 +146,7 @@ protected theorem ind {β : R[S⁻¹] → Prop} (c : ∀ (r : R) (s : S), β (r
 #align ore_localization.ind OreLocalization.ind
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.ore_div_eq_iff OreLocalization.oreDiv_eq_iffₓ'. -/
 theorem oreDiv_eq_iff {r₁ r₂ : R} {s₁ s₂ : S} :
     r₁ /ₒ s₁ = r₂ /ₒ s₂ ↔ ∃ (u : S)(v : R), r₂ * u = r₁ * v ∧ (s₂ : R) * u = s₁ * v :=
@@ -206,10 +203,7 @@ protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t
 #align ore_localization.eq_of_num_factor_eq OreLocalization.eq_of_num_factor_eq
 
 /- warning: ore_localization.lift_expand -> OreLocalization.liftExpand is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align ore_localization.lift_expand OreLocalization.liftExpandₓ'. -/
 /-- A function or predicate over `R` and `S` can be lifted to `R[S⁻¹]` if it is invariant
 under expansion on the right. -/
@@ -238,10 +232,7 @@ def liftExpand {C : Sort _} (P : R → S → C)
 #align ore_localization.lift_expand OreLocalization.liftExpand
 
 /- warning: ore_localization.lift_expand_of -> OreLocalization.liftExpand_of is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align ore_localization.lift_expand_of OreLocalization.liftExpand_ofₓ'. -/
 @[simp]
 theorem liftExpand_of {C : Sort _} {P : R → S → C}
@@ -251,10 +242,7 @@ theorem liftExpand_of {C : Sort _} {P : R → S → C}
 #align ore_localization.lift_expand_of OreLocalization.liftExpand_of
 
 /- warning: ore_localization.lift₂_expand -> OreLocalization.lift₂Expand is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.lift₂_expand OreLocalization.lift₂Expandₓ'. -/
 /-- A version of `lift_expand` used to simultaneously lift functions with two arguments
 in ``R[S⁻¹]`.-/
@@ -273,10 +261,7 @@ def lift₂Expand {C : Sort _} (P : R → S → R → S → C)
 #align ore_localization.lift₂_expand OreLocalization.lift₂Expand
 
 /- warning: ore_localization.lift₂_expand_of -> OreLocalization.lift₂Expand_of is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.lift₂_expand_of OreLocalization.lift₂Expand_ofₓ'. -/
 @[simp]
 theorem lift₂Expand_of {C : Sort _} {P : R → S → R → S → C}
@@ -290,7 +275,6 @@ theorem lift₂Expand_of {C : Sort _} {P : R → S → R → S → C}
 
 private def mul' (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) : R[S⁻¹] :=
   r₁ * oreNum r₂ s₁ /ₒ (s₂ * oreDenom r₂ s₁)
-#align ore_localization.mul' ore_localization.mul'
 
 private theorem mul'_char (r₁ r₂ : R) (s₁ s₂ : S) (u : S) (v : R) (huv : r₂ * (u : R) = s₁ * v) :
     mul' r₁ s₁ r₂ s₂ = r₁ * v /ₒ (s₂ * u) :=
@@ -311,7 +295,6 @@ private theorem mul'_char (r₁ r₂ : R) (s₁ s₂ : S) (u : S) (v : R) (huv :
     simp only [mul_assoc]
   · assoc_rw [h₃]
     simp only [mul_assoc]
-#align ore_localization.mul'_char ore_localization.mul'_char
 
 #print OreLocalization.mul /-
 /-- The multiplication on the Ore localization of monoids. -/
@@ -378,10 +361,7 @@ theorem oreDiv_mul_char (r₁ r₂ : R) (s₁ s₂ : S) (r' : R) (s' : S) (huv :
 #align ore_localization.ore_div_mul_char OreLocalization.oreDiv_mul_char
 
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 /-- Another characterization lemma for the multiplication on the Ore localizaion delivering
 Ore witnesses and conditions bundled in a sigma type. -/
@@ -513,10 +493,7 @@ protected theorem mul_cancel {r : R} {s t : S} : r /ₒ s * (s /ₒ t) = r /ₒ
 #align ore_localization.mul_cancel OreLocalization.mul_cancel
 
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 Case conversion may be inaccurate. Consider using '#align ore_localization.mul_cancel' OreLocalization.mul_cancel'ₓ'. -/
 @[simp]
 protected theorem mul_cancel' {r₁ r₂ : R} {s t : S} : r₁ /ₒ s * (s * r₂ /ₒ t) = r₁ * r₂ /ₒ t := by
@@ -595,10 +572,7 @@ variable (hf : ∀ s : S, f s = fS s)
 include f fS hf
 
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 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom OreLocalization.universalMulHomₓ'. -/
 /-- The universal lift from a morphism `R →* T`, which maps elements of `S` to units of `T`,
 to a morphism `R[S⁻¹] →* T`. -/
@@ -630,10 +604,7 @@ def universalMulHom : R[S⁻¹] →* T
 #align ore_localization.universal_mul_hom OreLocalization.universalMulHom
 
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(Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_apply OreLocalization.universalMulHom_applyₓ'. -/
 theorem universalMulHom_apply {r : R} {s : S} :
     universalMulHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
@@ -641,20 +612,14 @@ theorem universalMulHom_apply {r : R} {s : S} :
 #align ore_localization.universal_mul_hom_apply OreLocalization.universalMulHom_apply
 
 /- warning: ore_localization.universal_mul_hom_commutes -> OreLocalization.universalMulHom_commutes is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_commutes OreLocalization.universalMulHom_commutesₓ'. -/
 theorem universalMulHom_commutes {r : R} : universalMulHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_mul_hom_apply]
 #align ore_localization.universal_mul_hom_commutes OreLocalization.universalMulHom_commutes
 
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(OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) φ (OreLocalization.universalMulHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_unique OreLocalization.universalMulHom_uniqueₓ'. -/
 /-- The universal morphism `universal_mul_hom` is unique. -/
 theorem universalMulHom_unique (φ : R[S⁻¹] →* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
@@ -742,7 +707,6 @@ variable {R : Type _} [Semiring R] {S : Submonoid R} [OreSet S]
 
 private def add'' (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) : R[S⁻¹] :=
   (r₁ * oreDenom (s₁ : R) s₂ + r₂ * oreNum s₁ s₂) /ₒ (s₁ * oreDenom s₁ s₂)
-#align ore_localization.add'' ore_localization.add''
 
 private theorem add''_char (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) (rb : R) (sb : S)
     (hb : (s₁ : R) * sb = (s₂ : R) * rb) : add'' r₁ s₁ r₂ s₂ = (r₁ * sb + r₂ * rb) /ₒ (s₁ * sb) :=
@@ -773,7 +737,6 @@ private theorem add''_char (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) (rb : R)
     noncomm_ring
   · assoc_rw [hc]
     noncomm_ring
-#align ore_localization.add''_char ore_localization.add''_char
 
 attribute [local instance] OreLocalization.oreEqv
 
@@ -805,7 +768,6 @@ private def add' (r₂ : R) (s₂ : S) : R[S⁻¹] → R[S⁻¹] :=
     · simp
     · simp only [mul_one, Submonoid.coe_one, Submonoid.coe_mul] at this⊢
       assoc_rw [hc, this]
-#align ore_localization.add' ore_localization.add'
 
 private theorem add'_comm (r₁ r₂ : R) (s₁ s₂ : S) : add' r₁ s₁ (r₂ /ₒ s₂) = add' r₂ s₂ (r₁ /ₒ s₁) :=
   by
@@ -843,7 +805,6 @@ private theorem add'_comm (r₁ r₂ : R) (s₁ s₂ : S) : add' r₁ s₁ (r₂
     noncomm_ring
   · rw [mul_assoc, ← mul_assoc ↑sa, ← hd, hb]
     noncomm_ring
-#align ore_localization.add'_comm ore_localization.add'_comm
 
 /-- The addition on the Ore localization. -/
 private def add : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] := fun x =>
@@ -853,16 +814,12 @@ private def add : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] := fun x =>
       induction' x using OreLocalization.ind with r₃ s₃
       dsimp; rw [add'_comm, add'_comm r₂]
       simp [(· /ₒ ·), Quotient.sound hyz])
-#align ore_localization.add ore_localization.add
 
 instance : Add R[S⁻¹] :=
   ⟨add⟩
 
 /- warning: ore_localization.ore_div_add_ore_div -> OreLocalization.oreDiv_add_oreDiv is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align ore_localization.ore_div_add_ore_div OreLocalization.oreDiv_add_oreDivₓ'. -/
 theorem oreDiv_add_oreDiv {r r' : R} {s s' : S} :
     r /ₒ s + r' /ₒ s' = (r * oreDenom (s : R) s' + r' * oreNum s s') /ₒ (s * oreDenom s s') :=
@@ -870,10 +827,7 @@ theorem oreDiv_add_oreDiv {r r' : R} {s s' : S} :
 #align ore_localization.ore_div_add_ore_div OreLocalization.oreDiv_add_oreDiv
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.ore_div_add_char OreLocalization.oreDiv_add_charₓ'. -/
 /-- A characterization of the addition on the Ore localizaion, allowing for arbitrary Ore
 numerator and Ore denominator. -/
@@ -883,10 +837,7 @@ theorem oreDiv_add_char {r r' : R} (s s' : S) (rb : R) (sb : S) (h : (s : R) * s
 #align ore_localization.ore_div_add_char OreLocalization.oreDiv_add_char
 
 /- warning: ore_localization.ore_div_add_char' -> OreLocalization.oreDivAddChar' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.ore_div_add_char' OreLocalization.oreDivAddChar'ₓ'. -/
 /-- Another characterization of the addition on the Ore localization, bundling up all witnesses
 and conditions into a sigma type. -/
@@ -943,7 +894,6 @@ protected theorem add_assoc (x y z : R[S⁻¹]) : x + y + z = x + (y + z) :=
 
 private def zero : R[S⁻¹] :=
   0 /ₒ 1
-#align ore_localization.zero ore_localization.zero
 
 instance : Zero R[S⁻¹] :=
   ⟨zero⟩
@@ -1104,10 +1054,7 @@ variable (hf : ∀ s : S, f s = fS s)
 include f fS hf
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom OreLocalization.universalHomₓ'. -/
 /-- The universal lift from a ring homomorphism `f : R →+* T`, which maps elements in `S` to
 units of `T`, to a ring homomorphism `R[S⁻¹] →+* T`. This extends the construction on
@@ -1158,10 +1105,7 @@ def universalHom : R[S⁻¹] →+* T :=
 #align ore_localization.universal_hom OreLocalization.universalHom
 
 /- warning: ore_localization.universal_hom_apply -> OreLocalization.universalHom_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_apply OreLocalization.universalHom_applyₓ'. -/
 theorem universalHom_apply {r : R} {s : S} :
     universalHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
@@ -1169,20 +1113,14 @@ theorem universalHom_apply {r : R} {s : S} :
 #align ore_localization.universal_hom_apply OreLocalization.universalHom_apply
 
 /- warning: ore_localization.universal_hom_commutes -> OreLocalization.universalHom_commutes is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_commutes OreLocalization.universalHom_commutesₓ'. -/
 theorem universalHom_commutes {r : R} : universalHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_hom_apply]
 #align ore_localization.universal_hom_commutes OreLocalization.universalHom_commutes
 
 /- warning: ore_localization.universal_hom_unique -> OreLocalization.universalHom_unique is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_unique OreLocalization.universalHom_uniqueₓ'. -/
 theorem universalHom_unique (φ : R[S⁻¹] →+* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
     φ = universalHom f fS hf :=
@@ -1312,10 +1250,7 @@ instance : Inv R[R⁰⁻¹] :=
   ⟨OreLocalization.inv⟩
 
 /- warning: ore_localization.inv_def -> OreLocalization.inv_def is a dubious translation:
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-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))] {r : R} {s : Subtype.{succ u1} R (fun (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 _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) x (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))}, Eq.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (Inv.inv.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.inv'.{u1} R _inst_1 _inst_2 _inst_3 _inst_4) (OreLocalization.oreDiv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3 r s)) (dite.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (Eq.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Classical.propDecidable (Eq.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (fun (hr : Eq.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) => OfNat.ofNat.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) 0 (Zero.toOfNat0.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3) (OreLocalization.instZeroOreLocalizationToMonoidToMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_3))) (fun (hr : Not (Eq.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) => OreLocalization.oreDiv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _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 (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) s) (Subtype.mk.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) x (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) r (fun (_x : R) => eq_zero_of_ne_zero_of_mul_right_eq_zero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_4 r _x hr))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ore_localization.inv_def OreLocalization.inv_defₓ'. -/
 protected theorem inv_def {r : R} {s : R⁰} :
     (r /ₒ s)⁻¹ =

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

@@ -568,7 +568,7 @@ def numeratorHom : R →* R[S⁻¹] where
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R}, Eq.{succ u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) => R -> (OreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Submonoid.one.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) r) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.one.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S))))
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) r) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.one.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S))))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_hom_apply OreLocalization.numeratorHom_applyₓ'. -/
 theorem numeratorHom_apply {r : R} : numeratorHom r = r /ₒ (1 : S) :=
   rfl
@@ -578,7 +578,7 @@ theorem numeratorHom_apply {r : R} : numeratorHom r = r /ₒ (1 : S) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), IsUnit.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) => R -> (OreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S))))) s))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s))
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_is_unit OreLocalization.numerator_isUnitₓ'. -/
 theorem numerator_isUnit (s : S) : IsUnit (numeratorHom (s : R) : R[S⁻¹]) :=
   ⟨numeratorUnit s, rfl⟩
@@ -598,7 +598,7 @@ include f fS hf
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)), (forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S))))) s)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T _inst_3) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T _inst_3) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T _inst_3) T (coeBase.{succ u2, succ u2} (Units.{u2} T _inst_3) T (Units.hasCoe.{u2} T _inst_3)))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))) -> (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)), (forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)))) f (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (Units.val.{u2} T _inst_3 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => Units.{u2} T _inst_3) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (MulOneClass.toMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S)) (MulOneClass.toMul.{u2} (Units.{u2} T _inst_3) (Units.instMulOneClassUnits.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)))) fS s))) -> (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)), (forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)))) f (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (Units.val.{u2} T _inst_3 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => Units.{u2} T _inst_3) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (MulOneClass.toMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S)) (MulOneClass.toMul.{u2} (Units.{u2} T _inst_3) (Units.instMulOneClassUnits.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)))) fS s))) -> (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom OreLocalization.universalMulHomₓ'. -/
 /-- The universal lift from a morphism `R →* T`, which maps elements of `S` to units of `T`,
 to a morphism `R[S⁻¹] →* T`. -/
@@ -633,7 +633,7 @@ def universalMulHom : R[S⁻¹] →* T
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R 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HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T _inst_3) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T _inst_3) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T _inst_3) T (coeBase.{succ u2, succ u2} (Units.{u2} T _inst_3) T (Units.hasCoe.{u2} T _inst_3)))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))) {r : R} {s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R 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_inst_3)) (OreLocalization.universalMulHom.{u1, u2} R _inst_1 S _inst_2 T _inst_3 f fS hf) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r s)) (HMul.hMul.{u2, u2, u2} T T T (instHMul.{u2} T (MulOneClass.toHasMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f r) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T _inst_3) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T _inst_3) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T _inst_3) T (coeBase.{succ u2, succ u2} (Units.{u2} T _inst_3) T (Units.hasCoe.{u2} T _inst_3)))) (Inv.inv.{u2} (Units.{u2} T _inst_3) (Units.hasInv.{u2} T _inst_3) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f (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 (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) S)) s)) (Units.val.{u1} T _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (fun (_x : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => Units.{u1} T _inst_3) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) 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(Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))) {r : R} {s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R 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(Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))))
+  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f (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 (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) S)) s)) (Units.val.{u1} T _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (fun (_x : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} 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(Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))) {r : R} {s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) (OreLocalization.oreDiv.{u2} R _inst_1 S _inst_2 r s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) (fun (_x : OreLocalization.{u2} R _inst_1 S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S 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(Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)))) (OreLocalization.universalMulHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf) (OreLocalization.oreDiv.{u2} R _inst_1 S _inst_2 r s)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) r) T ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) r) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) r) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) r) _inst_3))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f r) (Units.val.{u1} T _inst_3 (Inv.inv.{u1} (Units.{u1} T _inst_3) (Units.instInv.{u1} T _inst_3) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => Units.{u1} T _inst_3) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) 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(Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_apply OreLocalization.universalMulHom_applyₓ'. -/
 theorem universalMulHom_apply {r : R} {s : S} :
     universalMulHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
@@ -644,7 +644,7 @@ theorem universalMulHom_apply {r : R} {s : S} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) 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+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (hf : forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R 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_inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)))) f r)
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_commutes OreLocalization.universalMulHom_commutesₓ'. -/
 theorem universalMulHom_commutes {r : R} : universalMulHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_mul_hom_apply]
@@ -654,7 +654,7 @@ theorem universalMulHom_commutes {r : R} : universalMulHom f fS hf (numeratorHom
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) 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(Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))) (φ : MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)), (forall (r : R), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) => (OreLocalization.{u1} R _inst_1 S _inst_2) -> T) (MonoidHom.hasCoeToFun.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) φ (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) => R -> (OreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f r)) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) φ (OreLocalization.universalMulHom.{u1, u2} R _inst_1 S _inst_2 T _inst_3 f fS hf))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f r)) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) φ (OreLocalization.universalMulHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
+  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (fun (_x : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} 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(Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))) (φ : MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)), (forall (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => OreLocalization.{u2} R _inst_1 S _inst_2) a) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (OreLocalization.{u2} R _inst_1 S _inst_2) (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u2} R _inst_1 S _inst_2) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) (fun (_x : OreLocalization.{u2} R _inst_1 S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) T (MulOneClass.toMul.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)))) φ (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => OreLocalization.{u2} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (OreLocalization.{u2} R _inst_1 S _inst_2) (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) 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(Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f r)) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) φ (OreLocalization.universalMulHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_unique OreLocalization.universalMulHom_uniqueₓ'. -/
 /-- The universal morphism `universal_mul_hom` is unique. -/
 theorem universalMulHom_unique (φ : R[S⁻¹] →* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
@@ -1107,7 +1107,7 @@ include f fS hf
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.mulOneClass.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))), (forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S), Eq.{succ u2} T (coeFn.{max (succ u1) (succ 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S)) (MulOneClass.toMul.{u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) fS s))) -> (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))), (forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (Units.val.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S)) (MulOneClass.toMul.{u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) fS s))) -> (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom OreLocalization.universalHomₓ'. -/
 /-- The universal lift from a ring homomorphism `f : R →+* T`, which maps elements in `S` to
 units of `T`, to a ring homomorphism `R[S⁻¹] →+* T`. This extends the construction on
@@ -1161,7 +1161,7 @@ def universalHom : R[S⁻¹] →+* T :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S))))) s)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (coeBase.{succ u2, succ u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (Units.hasCoe.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) 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 but is expected to have type
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(MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S)) (MulOneClass.toMul.{u1} (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))))) fS s))))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S] {T : Type.{u1}} [_inst_3 : Semiring.{u1} T] (f : RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (hf : forall (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) f (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) S)) s)) (Units.val.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (fun (_x : 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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) => Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R 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=> Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R 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 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_apply OreLocalization.universalHom_applyₓ'. -/
 theorem universalHom_apply {r : R} {s : S} :
     universalHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
@@ -1172,7 +1172,7 @@ theorem universalHom_apply {r : R} {s : S} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{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.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f r)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (hf : forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (Units.val.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S)) (MulOneClass.toMul.{u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) fS s))) {r : R}, Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) => T) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} 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_inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) r)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (fun (_x : OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (NonUnitalNonAssocSemiring.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R 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(Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f r)
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_commutes OreLocalization.universalHom_commutesₓ'. -/
 theorem universalHom_commutes {r : R} : universalHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_hom_apply]
@@ -1182,7 +1182,7 @@ theorem universalHom_commutes {r : R} : universalHom f fS hf (numeratorHom r) =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.mulOneClass.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S), Eq.{succ u2} T (coeFn.{max (succ u1) 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+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S] {T : Type.{u1}} [_inst_3 : Semiring.{u1} T] (f : RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R 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(NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R 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(OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) φ (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (MulOneClass.toMul.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2)) (MonoidHom.monoidHomClass.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))))) (OreLocalization.numeratorHom.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) f r)) -> (Eq.{max (succ u2) (succ u1)} (RingHom.{u2, u1} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) φ (OreLocalization.universalHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_unique OreLocalization.universalHom_uniqueₓ'. -/
 theorem universalHom_unique (φ : R[S⁻¹] →+* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
     φ = universalHom f fS hf :=
@@ -1243,7 +1243,7 @@ open nonZeroDivisors
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) => R -> (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (OreLocalization.numeratorHom.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_injₓ'. -/
 theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom : R → R[S⁻¹]) :=
   fun r₁ r₂ h =>

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

@@ -1241,7 +1241,7 @@ open nonZeroDivisors
 
 /- warning: ore_localization.numerator_hom_inj -> OreLocalization.numeratorHom_inj is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) => R -> (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (OreLocalization.numeratorHom.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) => R -> (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (OreLocalization.numeratorHom.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_injₓ'. -/
@@ -1256,7 +1256,7 @@ theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom :
 
 /- warning: ore_localization.nontrivial_of_non_zero_divisors -> OreLocalization.nontrivial_of_nonZeroDivisors is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S] [_inst_3 : 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 _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Nontrivial.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S] [_inst_3 : 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 _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Nontrivial.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S] [_inst_3 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Nontrivial.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))
 Case conversion may be inaccurate. Consider using '#align ore_localization.nontrivial_of_non_zero_divisors OreLocalization.nontrivial_of_nonZeroDivisorsₓ'. -/

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

@@ -1201,7 +1201,7 @@ variable {R : Type _} [Ring R] {S : Submonoid R} [OreSet S]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S], (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) -> (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) -> (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) -> (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)
 Case conversion may be inaccurate. Consider using '#align ore_localization.neg OreLocalization.negₓ'. -/
 /-- Negation on the Ore localization is defined via negation on the numerator. -/
 protected def neg : R[S⁻¹] → R[S⁻¹] :=
@@ -1216,7 +1216,7 @@ instance : Neg R[S⁻¹] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S] (r : R) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) S), Eq.{succ u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Neg.neg.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.hasNeg.{u1} R _inst_1 S _inst_2) (OreLocalization.oreDiv.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2 r s)) (OreLocalization.oreDiv.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2 (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) r) s)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S] (r : R) (s : Subtype.{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 _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) x S)), Eq.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Neg.neg.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instNegOreLocalizationToMonoidToMonoidWithZeroToSemiring.{u1} R _inst_1 S _inst_2) (OreLocalization.oreDiv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2 r s)) (OreLocalization.oreDiv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2 (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) r) s)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S] (r : R) (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) x S)), Eq.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Neg.neg.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instNegOreLocalizationToMonoidToMonoidWithZeroToSemiring.{u1} R _inst_1 S _inst_2) (OreLocalization.oreDiv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2 r s)) (OreLocalization.oreDiv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2 (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) r) s)
 Case conversion may be inaccurate. Consider using '#align ore_localization.neg_def OreLocalization.neg_defₓ'. -/
 @[simp]
 protected theorem neg_def (r : R) (s : S) : -(r /ₒ s) = -r /ₒ s :=
@@ -1227,7 +1227,7 @@ protected theorem neg_def (r : R) (s : S) : -(r /ₒ s) = -r /ₒ s :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S] (x : OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2), Eq.{succ u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (HAdd.hAdd.{u1, u1, u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (instHAdd.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.hasAdd.{u1} R (Ring.toSemiring.{u1} R _inst_1) S _inst_2)) (Neg.neg.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.hasNeg.{u1} R _inst_1 S _inst_2) x) x) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) 0 (OfNat.mk.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) 0 (Zero.zero.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.hasZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) S _inst_2))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S] (x : OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2), Eq.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (HAdd.hAdd.{u1, u1, u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (instHAdd.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instAddOreLocalizationToMonoidToMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) S _inst_2)) (Neg.neg.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instNegOreLocalizationToMonoidToMonoidWithZeroToSemiring.{u1} R _inst_1 S _inst_2) x) x) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) 0 (Zero.toOfNat0.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instZeroOreLocalizationToMonoidToMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) S _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S] (x : OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2), Eq.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (HAdd.hAdd.{u1, u1, u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (instHAdd.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instAddOreLocalizationToMonoidToMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) S _inst_2)) (Neg.neg.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instNegOreLocalizationToMonoidToMonoidWithZeroToSemiring.{u1} R _inst_1 S _inst_2) x) x) (OfNat.ofNat.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) 0 (Zero.toOfNat0.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instZeroOreLocalizationToMonoidToMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1) S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align ore_localization.add_left_neg OreLocalization.add_left_negₓ'. -/
 protected theorem add_left_neg (x : R[S⁻¹]) : -x + x = 0 := by
   induction' x using OreLocalization.ind with r s <;> simp
@@ -1243,7 +1243,7 @@ open nonZeroDivisors
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) => R -> (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (OreLocalization.numeratorHom.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_injₓ'. -/
 theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom : R → R[S⁻¹]) :=
   fun r₁ r₂ h =>
@@ -1258,7 +1258,7 @@ theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S] [_inst_3 : 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 _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Nontrivial.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S] [_inst_3 : 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 _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Nontrivial.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S] [_inst_3 : Nontrivial.{u1} R], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Nontrivial.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))
 Case conversion may be inaccurate. Consider using '#align ore_localization.nontrivial_of_non_zero_divisors OreLocalization.nontrivial_of_nonZeroDivisorsₓ'. -/
 theorem nontrivial_of_nonZeroDivisors [Nontrivial R] (hS : S ≤ R⁰) : Nontrivial R[S⁻¹] :=
   ⟨⟨0, 1, fun h => by

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

@@ -633,7 +633,7 @@ def universalMulHom : R[S⁻¹] →* T
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) 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 but is expected to have type
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(Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_apply OreLocalization.universalMulHom_applyₓ'. -/
 theorem universalMulHom_apply {r : R} {s : S} :
     universalMulHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
@@ -1161,7 +1161,7 @@ def universalHom : R[S⁻¹] →+* T :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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 but is expected to have type
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=> Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))))) fS s))))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S] {T : Type.{u1}} [_inst_3 : Semiring.{u1} T] (f : RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (hf : forall (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) f r) (Units.val.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (Inv.inv.{u1} (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Units.instInv.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (fun (_x : 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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) => Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S)) (MulOneClass.toMul.{u1} (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))))) fS s))))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_apply OreLocalization.universalHom_applyₓ'. -/
 theorem universalHom_apply {r : R} {s : S} :
     universalHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=

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

@@ -1214,7 +1214,7 @@ instance : Neg R[S⁻¹] :=
 
 /- warning: ore_localization.neg_def -> OreLocalization.neg_def is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S] (r : R) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) S), Eq.{succ u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Neg.neg.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.hasNeg.{u1} R _inst_1 S _inst_2) (OreLocalization.oreDiv.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2 r s)) (OreLocalization.oreDiv.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2 (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) r) s)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S] (r : R) (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) S), Eq.{succ u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Neg.neg.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.hasNeg.{u1} R _inst_1 S _inst_2) (OreLocalization.oreDiv.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2 r s)) (OreLocalization.oreDiv.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2 (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) r) s)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S] (r : R) (s : Subtype.{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 _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) x S)), Eq.{succ u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Neg.neg.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instNegOreLocalizationToMonoidToMonoidWithZeroToSemiring.{u1} R _inst_1 S _inst_2) (OreLocalization.oreDiv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2 r s)) (OreLocalization.oreDiv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2 (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_1) r) s)
 Case conversion may be inaccurate. Consider using '#align ore_localization.neg_def OreLocalization.neg_defₓ'. -/

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

@@ -568,7 +568,7 @@ def numeratorHom : R →* R[S⁻¹] where
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R}, Eq.{succ u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) => R -> (OreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Submonoid.one.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) r) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.one.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S))))
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) r) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.one.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S))))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_hom_apply OreLocalization.numeratorHom_applyₓ'. -/
 theorem numeratorHom_apply {r : R} : numeratorHom r = r /ₒ (1 : S) :=
   rfl
@@ -578,7 +578,7 @@ theorem numeratorHom_apply {r : R} : numeratorHom r = r /ₒ (1 : S) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), IsUnit.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) => R -> (OreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S))))) s))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s))
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_is_unit OreLocalization.numerator_isUnitₓ'. -/
 theorem numerator_isUnit (s : S) : IsUnit (numeratorHom (s : R) : R[S⁻¹]) :=
   ⟨numeratorUnit s, rfl⟩
@@ -598,7 +598,7 @@ include f fS hf
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)), (forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S))))) s)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T _inst_3) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T _inst_3) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T _inst_3) T (coeBase.{succ u2, succ u2} (Units.{u2} T _inst_3) T (Units.hasCoe.{u2} T _inst_3)))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))) -> (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)), (forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)))) f (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (Units.val.{u2} T _inst_3 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => Units.{u2} T _inst_3) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (MulOneClass.toMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S)) (MulOneClass.toMul.{u2} (Units.{u2} T _inst_3) (Units.instMulOneClassUnits.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)))) fS s))) -> (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)), (forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)))) f (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (Units.val.{u2} T _inst_3 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => Units.{u2} T _inst_3) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (MulOneClass.toMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S)) (MulOneClass.toMul.{u2} (Units.{u2} T _inst_3) (Units.instMulOneClassUnits.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)))) fS s))) -> (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom OreLocalization.universalMulHomₓ'. -/
 /-- The universal lift from a morphism `R →* T`, which maps elements of `S` to units of `T`,
 to a morphism `R[S⁻¹] →* T`. -/
@@ -633,7 +633,7 @@ def universalMulHom : R[S⁻¹] →* T
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R 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 but is expected to have type
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(Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))))
+  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))) {r : R} {s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) (OreLocalization.oreDiv.{u2} R _inst_1 S _inst_2 r s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) (fun (_x : OreLocalization.{u2} R _inst_1 S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S 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(Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)))) (OreLocalization.universalMulHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf) (OreLocalization.oreDiv.{u2} R _inst_1 S _inst_2 r s)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) r) T ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) r) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) r) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) r) _inst_3))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f r) (Units.val.{u1} T _inst_3 (Inv.inv.{u1} (Units.{u1} T _inst_3) (Units.instInvUnits.{u1} T _inst_3) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => Units.{u1} T _inst_3) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) 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(Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_apply OreLocalization.universalMulHom_applyₓ'. -/
 theorem universalMulHom_apply {r : R} {s : S} :
     universalMulHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
@@ -644,7 +644,7 @@ theorem universalMulHom_apply {r : R} {s : S} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) 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u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)))) f r)
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_commutes OreLocalization.universalMulHom_commutesₓ'. -/
 theorem universalMulHom_commutes {r : R} : universalMulHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_mul_hom_apply]
@@ -654,7 +654,7 @@ theorem universalMulHom_commutes {r : R} : universalMulHom f fS hf (numeratorHom
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) 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HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T _inst_3) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T _inst_3) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T _inst_3) T (coeBase.{succ u2, succ u2} (Units.{u2} T _inst_3) T (Units.hasCoe.{u2} T _inst_3)))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))) (φ : MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)), (forall (r : R), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) => (OreLocalization.{u1} R _inst_1 S _inst_2) -> T) (MonoidHom.hasCoeToFun.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) φ (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) => R -> (OreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f r)) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) φ (OreLocalization.universalMulHom.{u1, u2} R _inst_1 S _inst_2 T _inst_3 f fS hf))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))) (φ : MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)), (forall (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u2} R _inst_1 S _inst_2) a) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (OreLocalization.{u2} R _inst_1 S _inst_2) (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u2} R _inst_1 S _inst_2) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) (fun (_x : OreLocalization.{u2} R _inst_1 S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) T (MulOneClass.toMul.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)))) φ (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u2} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (OreLocalization.{u2} R _inst_1 S _inst_2) (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) 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(Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f r)) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) φ (OreLocalization.universalMulHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_unique OreLocalization.universalMulHom_uniqueₓ'. -/
 /-- The universal morphism `universal_mul_hom` is unique. -/
 theorem universalMulHom_unique (φ : R[S⁻¹] →* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
@@ -1107,7 +1107,7 @@ include f fS hf
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.mulOneClass.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))), (forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S), Eq.{succ u2} T (coeFn.{max (succ u1) (succ 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 but is expected to have type
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(Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R 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(MulOneClass.toMul.{u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) fS s))) -> (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))), (forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (Units.val.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S)) (MulOneClass.toMul.{u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) fS s))) -> (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom OreLocalization.universalHomₓ'. -/
 /-- The universal lift from a ring homomorphism `f : R →+* T`, which maps elements in `S` to
 units of `T`, to a ring homomorphism `R[S⁻¹] →+* T`. This extends the construction on
@@ -1161,7 +1161,7 @@ def universalHom : R[S⁻¹] →+* T :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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 but is expected to have type
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(Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R 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(Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S)) (MulOneClass.toMul.{u1} (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))))) fS s))))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S] {T : Type.{u1}} [_inst_3 : Semiring.{u1} T] (f : RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (hf : forall (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) f (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) S)) s)) (Units.val.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (fun (_x : 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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) => Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R 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(Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S)) (MulOneClass.toMul.{u1} (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))))) fS s))))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_apply OreLocalization.universalHom_applyₓ'. -/
 theorem universalHom_apply {r : R} {s : S} :
     universalHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
@@ -1172,7 +1172,7 @@ theorem universalHom_apply {r : R} {s : S} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.mulOneClass.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S), Eq.{succ u2} T (coeFn.{max (succ u1) 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(SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S))))) s)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (coeBase.{succ u2, succ u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (Units.hasCoe.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) 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 but is expected to have type
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_inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) r)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (fun (_x : OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (NonUnitalNonAssocSemiring.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R 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(Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) (OreLocalization.universalHom.{u1, u2} R _inst_1 S _inst_2 T _inst_3 f fS hf) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) 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(OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) r)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f r)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (hf : forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (Units.val.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S)) (MulOneClass.toMul.{u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) fS s))) {r : R}, Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) => T) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} 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(MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S 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(Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f r)
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_commutes OreLocalization.universalHom_commutesₓ'. -/
 theorem universalHom_commutes {r : R} : universalHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_hom_apply]
@@ -1182,7 +1182,7 @@ theorem universalHom_commutes {r : R} : universalHom f fS hf (numeratorHom r) =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.mulOneClass.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S), Eq.{succ u2} T (coeFn.{max (succ u1) 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(OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) φ (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R 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(Semiring.toNonAssocSemiring.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) f r)) -> (Eq.{max (succ u2) (succ u1)} (RingHom.{u2, u1} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) φ (OreLocalization.universalHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S] {T : Type.{u1}} [_inst_3 : Semiring.{u1} T] (f : RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R 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(NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R 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T (Semiring.toNonAssocSemiring.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) φ (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (MulOneClass.toMul.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2)) (MonoidHom.monoidHomClass.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))))) (OreLocalization.numeratorHom.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) f r)) -> (Eq.{max (succ u2) (succ u1)} (RingHom.{u2, u1} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) φ (OreLocalization.universalHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_unique OreLocalization.universalHom_uniqueₓ'. -/
 theorem universalHom_unique (φ : R[S⁻¹] →+* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
     φ = universalHom f fS hf :=
@@ -1243,7 +1243,7 @@ open nonZeroDivisors
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) => R -> (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (OreLocalization.numeratorHom.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_injₓ'. -/
 theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom : R → R[S⁻¹]) :=
   fun r₁ r₂ h =>

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

@@ -1303,7 +1303,7 @@ protected def inv : R[R⁰⁻¹] → R[R⁰⁻¹] :=
       · by_cases ht : t = 0
         · exfalso
           apply nonZeroDivisors.coe_ne_zero ⟨_, hst⟩
-          simp [ht, mul_zero]
+          simp [ht, MulZeroClass.mul_zero]
         · simp only [hr, ht, [anonymous], dif_neg, not_false_iff, or_self_iff, mul_eq_zero]
           apply OreLocalization.expand)
 #align ore_localization.inv OreLocalization.inv

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

@@ -568,7 +568,7 @@ def numeratorHom : R →* R[S⁻¹] where
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R}, Eq.{succ u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) => R -> (OreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (OfNat.ofNat.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) 1 (OfNat.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) 1 (One.one.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Submonoid.one.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) r) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.one.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S))))
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {r : R}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) r) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.one.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S))))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_hom_apply OreLocalization.numeratorHom_applyₓ'. -/
 theorem numeratorHom_apply {r : R} : numeratorHom r = r /ₒ (1 : S) :=
   rfl
@@ -578,7 +578,7 @@ theorem numeratorHom_apply {r : R} : numeratorHom r = r /ₒ (1 : S) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), IsUnit.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) => R -> (OreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S))))) s))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s))
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_is_unit OreLocalization.numerator_isUnitₓ'. -/
 theorem numerator_isUnit (s : S) : IsUnit (numeratorHom (s : R) : R[S⁻¹]) :=
   ⟨numeratorUnit s, rfl⟩
@@ -598,7 +598,7 @@ include f fS hf
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)), (forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S))))) s)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T _inst_3) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T _inst_3) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T _inst_3) T (coeBase.{succ u2, succ u2} (Units.{u2} T _inst_3) T (Units.hasCoe.{u2} T _inst_3)))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))) -> (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)), (forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => T) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)))) f (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (Units.val.{u2} T _inst_3 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => Units.{u2} T _inst_3) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (MulOneClass.toMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S)) (MulOneClass.toMul.{u2} (Units.{u2} T _inst_3) (Units.instMulOneClassUnits.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)))) fS s))) -> (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)), (forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)))) f (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 _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) S)) s)) (Units.val.{u2} T _inst_3 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) => Units.{u2} T _inst_3) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (MulOneClass.toMul.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S)) (MulOneClass.toMul.{u2} (Units.{u2} T _inst_3) (Units.instMulOneClassUnits.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)))) fS s))) -> (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom OreLocalization.universalMulHomₓ'. -/
 /-- The universal lift from a morphism `R →* T`, which maps elements of `S` to units of `T`,
 to a morphism `R[S⁻¹] →* T`. -/
@@ -633,7 +633,7 @@ def universalMulHom : R[S⁻¹] →* T
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R 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(Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))) {r : R} {s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R 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_inst_3)) (OreLocalization.universalMulHom.{u1, u2} R _inst_1 S _inst_2 T _inst_3 f fS hf) (OreLocalization.oreDiv.{u1} R _inst_1 S _inst_2 r s)) (HMul.hMul.{u2, u2, u2} T T T (instHMul.{u2} T (MulOneClass.toHasMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f r) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T _inst_3) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T _inst_3) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T _inst_3) T (coeBase.{succ u2, succ u2} (Units.{u2} T _inst_3) T (Units.hasCoe.{u2} T _inst_3)))) (Inv.inv.{u2} (Units.{u2} T _inst_3) (Units.hasInv.{u2} T _inst_3) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f (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 (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) S)) s)) (Units.val.{u1} T _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (fun (_x : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => Units.{u1} T _inst_3) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) 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(Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))) {r : R} {s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R 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(Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))))
+  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f (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 (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) S)) s)) (Units.val.{u1} T _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (fun (_x : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} 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(Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))) {r : R} {s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) (OreLocalization.oreDiv.{u2} R _inst_1 S _inst_2 r s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) (fun (_x : OreLocalization.{u2} R _inst_1 S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S 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(Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)))) (OreLocalization.universalMulHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf) (OreLocalization.oreDiv.{u2} R _inst_1 S _inst_2 r s)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) r) T ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) r) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) r) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) r) _inst_3))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f r) (Units.val.{u1} T _inst_3 (Inv.inv.{u1} (Units.{u1} T _inst_3) (Units.instInvUnits.{u1} T _inst_3) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => Units.{u1} T _inst_3) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) 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(Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_apply OreLocalization.universalMulHom_applyₓ'. -/
 theorem universalMulHom_apply {r : R} {s : S} :
     universalMulHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
@@ -644,7 +644,7 @@ theorem universalMulHom_apply {r : R} {s : S} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) 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+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) x S)) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.instMulOneClassUnits.{u2} T _inst_3)) (hf : forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R 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_inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))) R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (MulOneClass.toMul.{u2} T (Monoid.toMulOneClass.{u2} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3) (MonoidHom.monoidHomClass.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)))) f r)
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_commutes OreLocalization.universalMulHom_commutesₓ'. -/
 theorem universalMulHom_commutes {r : R} : universalMulHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_mul_hom_apply]
@@ -654,7 +654,7 @@ theorem universalMulHom_commutes {r : R} : universalMulHom f fS hf (numeratorHom
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] {S : Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u1} R _inst_1 S] {T : Type.{u2}} [_inst_3 : Monoid.{u2} T] (f : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f ((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 _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) 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(Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) -> (Units.{u2} T _inst_3)) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) R (Submonoid.setLike.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1))) S) (Units.{u2} T _inst_3) (Submonoid.toMulOneClass.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1) S) (Units.mulOneClass.{u2} T _inst_3)) fS s))) (φ : MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)), (forall (r : R), Eq.{succ u2} T (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) => (OreLocalization.{u1} R _inst_1 S _inst_2) -> T) (MonoidHom.hasCoeToFun.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) φ (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) => R -> (OreLocalization.{u1} R _inst_1 S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2))) (OreLocalization.numeratorHom.{u1} R _inst_1 S _inst_2) r)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) (fun (_x : MonoidHom.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) => R -> T) (MonoidHom.hasCoeToFun.{u1, u2} R T (Monoid.toMulOneClass.{u1} R _inst_1) (Monoid.toMulOneClass.{u2} T _inst_3)) f r)) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u1, u2} (OreLocalization.{u1} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R _inst_1 S _inst_2) (OreLocalization.monoid.{u1} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u2} T _inst_3)) φ (OreLocalization.universalMulHom.{u1, u2} R _inst_1 S _inst_2 T _inst_3 f fS hf))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f r)) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) φ (OreLocalization.universalMulHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
+  forall {R : Type.{u2}} [_inst_1 : Monoid.{u2} R] {S : Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)} [_inst_2 : OreLocalization.OreSet.{u2} R _inst_1 S] {T : Type.{u1}} [_inst_3 : Monoid.{u1} T] (f : MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (hf : forall (s : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R 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(Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (fun (_x : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} 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(Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) R (Submonoid.instSetLikeSubmonoid.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1))) x S)) (Units.{u1} T _inst_3) (Submonoid.toMulOneClass.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1) S) (Units.instMulOneClassUnits.{u1} T _inst_3)))) fS s))) (φ : MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)), (forall (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u2} R _inst_1 S _inst_2) a) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (OreLocalization.{u2} R _inst_1 S _inst_2) (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (MonoidHom.monoidHomClass.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))))) (OreLocalization.numeratorHom.{u2} R _inst_1 S _inst_2) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) (fun (_x : OreLocalization.{u2} R _inst_1 S _inst_2) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : OreLocalization.{u2} R _inst_1 S _inst_2) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) T (MulOneClass.toMul.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)))) φ (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u2} R _inst_1 S _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2))) R (OreLocalization.{u2} R _inst_1 S _inst_2) (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) 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(Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R _inst_1)) (MulOneClass.toMul.{u1} T (Monoid.toMulOneClass.{u1} T _inst_3)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)) R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3) (MonoidHom.monoidHomClass.{u2, u1} R T (Monoid.toMulOneClass.{u2} R _inst_1) (Monoid.toMulOneClass.{u1} T _inst_3)))) f r)) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (OreLocalization.{u2} R _inst_1 S _inst_2) T (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R _inst_1 S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R _inst_1 S _inst_2)) (Monoid.toMulOneClass.{u1} T _inst_3)) φ (OreLocalization.universalMulHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_mul_hom_unique OreLocalization.universalMulHom_uniqueₓ'. -/
 /-- The universal morphism `universal_mul_hom` is unique. -/
 theorem universalMulHom_unique (φ : R[S⁻¹] →* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
@@ -1107,7 +1107,7 @@ include f fS hf
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.mulOneClass.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))), (forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S), Eq.{succ u2} T (coeFn.{max (succ u1) (succ 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(MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S)) (MulOneClass.toMul.{u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) fS s))) -> (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))), (forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (Units.val.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S)) (MulOneClass.toMul.{u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) fS s))) -> (RingHom.{u1, u2} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u1} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u2} T _inst_3))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom OreLocalization.universalHomₓ'. -/
 /-- The universal lift from a ring homomorphism `f : R →+* T`, which maps elements in `S` to
 units of `T`, to a ring homomorphism `R[S⁻¹] →+* T`. This extends the construction on
@@ -1161,7 +1161,7 @@ def universalHom : R[S⁻¹] →+* T :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S))))) s)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (coeBase.{succ u2, succ u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) T (Units.hasCoe.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) 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 but is expected to have type
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(MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S)) (MulOneClass.toMul.{u1} (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))))) fS s))))
+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S] {T : Type.{u1}} [_inst_3 : Semiring.{u1} T] (f : RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (hf : forall (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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) f (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) S)) s)) (Units.val.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (fun (_x : 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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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 _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) => Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R 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=> Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) x S)) (Units.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3))) (Submonoid.toMulOneClass.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) S) (Units.instMulOneClassUnits.{u1} T (MonoidWithZero.toMonoid.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)))) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R 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 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_apply OreLocalization.universalHom_applyₓ'. -/
 theorem universalHom_apply {r : R} {s : S} :
     universalHom f fS hf (r /ₒ s) = f r * ((fS s)⁻¹ : Units T) :=
@@ -1172,7 +1172,7 @@ theorem universalHom_apply {r : R} {s : S} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{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.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f r)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (hf : forall (s : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f (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 _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) S)) s)) (Units.val.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (fun (_x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) => Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MulOneClass.toMul.{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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S)) (MulOneClass.toMul.{u2} (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (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 _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x S)) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.instMulOneClassUnits.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))))) fS s))) {r : R}, Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) => T) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (MulOneClass.toMul.{u1} 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(Semiring.toNonAssocSemiring.{u2} T _inst_3))))) f r)
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_commutes OreLocalization.universalHom_commutesₓ'. -/
 theorem universalHom_commutes {r : R} : universalHom f fS hf (numeratorHom r) = f r := by
   simp [numerator_hom_apply, universal_hom_apply]
@@ -1182,7 +1182,7 @@ theorem universalHom_commutes {r : R} : universalHom f fS hf (numeratorHom r) =
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) S] {T : Type.{u2}} [_inst_3 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_3)) (fS : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S) (Units.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3))) (Submonoid.toMulOneClass.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) S) (Units.mulOneClass.{u2} T (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T _inst_3)))) (hf : forall (s : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{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 _inst_1)))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) S), Eq.{succ u2} T (coeFn.{max (succ u1) 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+  forall {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))} [_inst_2 : OreLocalization.OreSet.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S] {T : Type.{u1}} [_inst_3 : Semiring.{u1} T] (f : RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (fS : MonoidHom.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R 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(OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) φ (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (MulOneClass.toMul.{u2} R (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (MulOneClass.toMul.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))) R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2)) (MonoidHom.monoidHomClass.{u2, u2} R (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (Monoid.toMulOneClass.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Monoid.toMulOneClass.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2))))) (OreLocalization.numeratorHom.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R T (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u1} T _inst_3))))) f r)) -> (Eq.{max (succ u2) (succ u1)} (RingHom.{u2, u1} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) T (Semiring.toNonAssocSemiring.{u2} (OreLocalization.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) S _inst_2) (OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero.{u2} R _inst_1 S _inst_2)) (Semiring.toNonAssocSemiring.{u1} T _inst_3)) φ (OreLocalization.universalHom.{u2, u1} R _inst_1 S _inst_2 T _inst_3 f fS hf))
 Case conversion may be inaccurate. Consider using '#align ore_localization.universal_hom_unique OreLocalization.universalHom_uniqueₓ'. -/
 theorem universalHom_unique (φ : R[S⁻¹] →+* T) (huniv : ∀ r : R, φ (numeratorHom r) = f r) :
     φ = universalHom f fS hf :=
@@ -1243,7 +1243,7 @@ open nonZeroDivisors
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (Ring.toMonoid.{u1} R _inst_1) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (fun (_x : MonoidHom.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) => R -> (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)) (MonoidHom.hasCoeToFun.{u1, u1} R (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (Monoid.toMulOneClass.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2) (OreLocalization.monoid.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2))) (OreLocalization.numeratorHom.{u1} R (Ring.toMonoid.{u1} R _inst_1) S _inst_2)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))} [_inst_2 : OreLocalization.OreSet.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{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 _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) -> (Function.Injective.{succ u1, succ u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (MulOneClass.toMul.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))) R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)) (MonoidHom.monoidHomClass.{u1, u1} R (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (Monoid.toMulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u1} (OreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2) (OreLocalization.instMonoidOreLocalization.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2))))) (OreLocalization.numeratorHom.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) S _inst_2)))
 Case conversion may be inaccurate. Consider using '#align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_injₓ'. -/
 theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom : R → R[S⁻¹]) :=
   fun r₁ r₂ h =>

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

These · are scoping when there is a single active goal.

These were found using a modification of the linter at #12339.

@@ -636,11 +636,11 @@ protected theorem add_assoc (x y z : R[S⁻¹]) : x + y + z = x + (y + z) := by
       ← OreLocalization.expand', Subtype.coe_eq_of_eq_mk ha, ← OreLocalization.expand]
     apply OreLocalization.expand'
   · rcases oreCondition (sd : R) (sa * sc) with ⟨re, _, _⟩
-    · simp_rw [← Submonoid.coe_mul] at hb hc hd
-      rw [← mul_assoc, Subtype.coe_eq_of_eq_mk hc]
-      rw [← OreLocalization.expand, Subtype.coe_eq_of_eq_mk hd, ← mul_assoc, ←
-        OreLocalization.expand, Subtype.coe_eq_of_eq_mk hb]
-      apply OreLocalization.expand
+    simp_rw [← Submonoid.coe_mul] at hb hc hd
+    rw [← mul_assoc, Subtype.coe_eq_of_eq_mk hc]
+    rw [← OreLocalization.expand, Subtype.coe_eq_of_eq_mk hd, ← mul_assoc, ←
+      OreLocalization.expand, Subtype.coe_eq_of_eq_mk hb]
+    apply OreLocalization.expand
 #align ore_localization.add_assoc OreLocalization.add_assoc
 
 private def zero : R[S⁻¹] :=

Define the canonical coercion from the nonnegative rationals to any division semiring.

From LeanAPAP

@@ -928,6 +928,7 @@ instance divisionRing : DivisionRing R[R⁰⁻¹] where
   __ := inv'
   mul_inv_cancel := OreLocalization.mul_inv_cancel
   inv_zero := OreLocalization.inv_zero
+  nnqsmul := _
   qsmul := _
 
 end DivisionRing

This is the parts of the diff of #11203 which don't mention NNRat.cast.

• Use more where notation.
• Write qsmul := _ instead of qsmul := qsmulRec _ to make the instances more robust to definition changes.
• Delete qsmulRec.
• Move qsmul before ratCast_def in instance declarations.
• Name more instances.
• Rename rat_smul to qsmul.

@@ -922,13 +922,13 @@ protected theorem inv_zero : (0 : R[R⁰⁻¹])⁻¹ = 0 := by
   simp
 #align ore_localization.inv_zero OreLocalization.inv_zero
 
-instance divisionRing : DivisionRing R[R⁰⁻¹] :=
-  { OreLocalization.nontrivial,
-    OreLocalization.inv',
-    OreLocalization.ring with
-    mul_inv_cancel := OreLocalization.mul_inv_cancel
-    inv_zero := OreLocalization.inv_zero
-    qsmul := qsmulRec _ }
+instance divisionRing : DivisionRing R[R⁰⁻¹] where
+  __ := ring
+  __ := nontrivial
+  __ := inv'
+  mul_inv_cancel := OreLocalization.mul_inv_cancel
+  inv_zero := OreLocalization.inv_zero
+  qsmul := _
 
 end DivisionRing
 

This subsumes some of the notes in #10752 and #10971. I'm on the fence as to whether replacing the dsimp only by beta_reduce is useful; this is easy to revert if needed.

@@ -378,21 +378,22 @@ variable (hf : ∀ s : S, f s = fS s)
 
 /-- The universal lift from a morphism `R →* T`, which maps elements of `S` to units of `T`,
 to a morphism `R[S⁻¹] →* T`. -/
-def universalMulHom : R[S⁻¹] →* T
-    where
-  -- Porting note: `simp only []` required for beta reductions
+def universalMulHom : R[S⁻¹] →* T where
+  -- Porting note(#12129): additional beta reduction needed
   toFun x :=
     x.liftExpand (fun r s => f r * ((fS s)⁻¹ : Units T)) fun r t s ht => by
-      simp only []
+      beta_reduce
       have : (fS ⟨s * t, ht⟩ : T) = fS s * f t := by
         simp only [← hf, MonoidHom.map_mul]
       conv_rhs =>
         rw [MonoidHom.map_mul, ← mul_one (f r), ← Units.val_one, ← mul_left_inv (fS s)]
         rw [Units.val_mul, ← mul_assoc, mul_assoc _ (fS s : T), ← this, mul_assoc]
       simp only [mul_one, Units.mul_inv]
-  map_one' := by simp only []; rw [OreLocalization.one_def, liftExpand_of]; simp
+  map_one' := by beta_reduce; rw [OreLocalization.one_def, liftExpand_of]; simp
   map_mul' x y := by
-    simp only []
+    -- Porting note: `simp only []` required, not just for beta reductions
+    beta_reduce
+    simp only [] -- TODO more!
     induction' x using OreLocalization.ind with r₁ s₁
     induction' y using OreLocalization.ind with r₂ s₂
     rcases oreDivMulChar' r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩; rw [ha']; clear ha'
@@ -822,8 +823,8 @@ variable {R : Type*} [Ring R] {S : Submonoid R} [OreSet S]
 /-- Negation on the Ore localization is defined via negation on the numerator. -/
 protected def neg : R[S⁻¹] → R[S⁻¹] :=
   liftExpand (fun (r : R) (s : S) => -r /ₒ s) fun r t s ht => by
-    -- Porting note: `simp only []` required for beta reductions
-    simp only []
+    -- Porting note(#12129): additional beta reduction needed
+    beta_reduce
     rw [neg_mul_eq_neg_mul, ← OreLocalization.expand]
 #align ore_localization.neg OreLocalization.neg
 

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

@@ -95,7 +95,6 @@ def oreDiv (r : R) (s : S) : R[S⁻¹] :=
   Quotient.mk' (r, s)
 #align ore_localization.ore_div OreLocalization.oreDiv
 
--- mathport name: «expr /ₒ »
 @[inherit_doc]
 infixl:70 " /ₒ " => oreDiv
 

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)

@@ -80,7 +80,6 @@ namespace OreLocalization
 section Monoid
 
 variable {R : Type*} [Monoid R] {S : Submonoid R}
-
 variable (R S) [OreSet S]
 
 @[inherit_doc OreLocalization]
@@ -375,9 +374,7 @@ theorem numerator_isUnit (s : S) : IsUnit (numeratorHom (s : R) : R[S⁻¹]) :=
 section UMP
 
 variable {T : Type*} [Monoid T]
-
 variable (f : R →* T) (fS : S →* Units T)
-
 variable (hf : ∀ s : S, f s = fS s)
 
 /-- The universal lift from a morphism `R →* T`, which maps elements of `S` to units of `T`,
@@ -746,9 +743,7 @@ instance instSemiringOreLocalization : Semiring R[S⁻¹] :=
 section UMP
 
 variable {T : Type*} [Semiring T]
-
 variable (f : R →+* T) (fS : S →* Units T)
-
 variable (hf : ∀ s : S, f s = fS s)
 
 /-- The universal lift from a ring homomorphism `f : R →+* T`, which maps elements in `S` to

Follows on from #6262. Again, this does not attempt to fix any diamonds; it only identifies where they may be.

@@ -932,7 +932,8 @@ instance divisionRing : DivisionRing R[R⁰⁻¹] :=
     OreLocalization.inv',
     OreLocalization.ring with
     mul_inv_cancel := OreLocalization.mul_inv_cancel
-    inv_zero := OreLocalization.inv_zero }
+    inv_zero := OreLocalization.inv_zero
+    qsmul := qsmulRec _ }
 
 end DivisionRing
 

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

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

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

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

@@ -679,7 +679,8 @@ instance instAddCommMonoidOreLocalization : AddCommMonoid R[S⁻¹] :=
     add_assoc := OreLocalization.add_assoc
     zero := zero
     zero_add := OreLocalization.zero_add
-    add_zero := fun x => by rw [OreLocalization.add_comm, OreLocalization.zero_add] }
+    add_zero := fun x => by rw [OreLocalization.add_comm, OreLocalization.zero_add]
+    nsmul := nsmulRec }
 
 protected theorem zero_mul (x : R[S⁻¹]) : 0 * x = 0 := by
   induction' x using OreLocalization.ind with r s
@@ -847,7 +848,8 @@ protected theorem add_left_neg (x : R[S⁻¹]) : -x + x = 0 := by
 instance ring : Ring R[S⁻¹] :=
   { OreLocalization.instSemiringOreLocalization,
     OreLocalization.instNegOreLocalization with
-    add_left_neg := OreLocalization.add_left_neg }
+    add_left_neg := OreLocalization.add_left_neg
+    zsmul := zsmulRec }
 
 open nonZeroDivisors
 

Classifies by adding issue number #11215 to porting notes claiming "TODO".

@@ -129,7 +129,7 @@ those factors expand to equal elements of `R`. -/
 protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t = r' * t) :
     r₁ * r * r₂ /ₒ s = r₁ * r' * r₂ /ₒ s := by
   rcases oreCondition r₂ t with ⟨r₂', t', hr₂⟩
-  -- Porting note: todo: use `assoc_rw`?
+  -- Porting note (#11215): TODO: use `assoc_rw`?
   calc
     r₁ * r * r₂ /ₒ s = r₁ * r * r₂ * t' /ₒ (s * t') := OreLocalization.expand (r₁ * r * r₂) s t' _
     _ = r₁ * r * (r₂ * t') /ₒ (s * t') := by simp [← mul_assoc]

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -871,7 +871,7 @@ noncomputable section DivisionRing
 
 open nonZeroDivisors
 
-open Classical
+open scoped Classical
 
 variable {R : Type*} [Ring R] [Nontrivial R] [OreSet R⁰]
 

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".

@@ -55,7 +55,7 @@ def oreEqv : Setoid (R × S) where
       rcases oreCondition (s : R) s' with ⟨r₂, s₂, h₁⟩
       rcases oreCondition r₂ u with ⟨r₃, s₃, h₂⟩
       have : (s : R) * ((v : R) * r₃) = (s : R) * (s₂ * s₃) := by
-        -- porting note: the proof used `assoc_rw`
+        -- Porting note: the proof used `assoc_rw`
         rw [← mul_assoc _ (s₂ : R), h₁, mul_assoc, h₂, ← mul_assoc, ← hsu, mul_assoc]
       rcases ore_left_cancel (v * r₃) (s₂ * s₃) s this with ⟨w, hw⟩
       refine ⟨s₂ * s₃ * w, u * r₃ * w, ?_, ?_⟩ <;> simp only [Submonoid.coe_mul, ← hw]
@@ -129,7 +129,7 @@ those factors expand to equal elements of `R`. -/
 protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t = r' * t) :
     r₁ * r * r₂ /ₒ s = r₁ * r' * r₂ /ₒ s := by
   rcases oreCondition r₂ t with ⟨r₂', t', hr₂⟩
-  -- porting note: todo: use `assoc_rw`?
+  -- Porting note: todo: use `assoc_rw`?
   calc
     r₁ * r * r₂ /ₒ s = r₁ * r * r₂ * t' /ₒ (s * t') := OreLocalization.expand (r₁ * r * r₂) s t' _
     _ = r₁ * r * (r₂ * t') /ₒ (s * t') := by simp [← mul_assoc]

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -151,8 +151,7 @@ def liftExpand {C : Sort*} (P : R → S → C)
     have s₁vS : (s₁ : R) * v ∈ S := by
       rw [← hs₂, ← S.coe_mul]
       exact SetLike.coe_mem (s₂ * u)
-    replace hs₂ : s₂ * u = ⟨(s₁ : R) * v, s₁vS⟩
-    · ext; simp [hs₂]
+    replace hs₂ : s₂ * u = ⟨(s₁ : R) * v, s₁vS⟩ := by ext; simp [hs₂]
     rw [hP r₁ v s₁ s₁vS, hP r₂ u s₂ (by norm_cast; rwa [hs₂]), hr₂]
     simp only [← hs₂]; rfl
 #align ore_localization.lift_expand OreLocalization.liftExpand

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob von Raumer, Kevin Klinge
 -/
 import Mathlib.GroupTheory.MonoidLocalization
-import Mathlib.RingTheory.NonZeroDivisors
+import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
 import Mathlib.RingTheory.OreLocalization.OreSet
 import Mathlib.Tactic.NoncommRing
 

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>

@@ -463,21 +463,16 @@ protected def localizationMap : S.LocalizationMap R[S⁻¹]
     induction' z using OreLocalization.ind with r s
     use (r, s); dsimp
     rw [numeratorHom_apply, numeratorHom_apply]; simp
-  eq_iff_exists' r₁ r₂ := by
-    dsimp; constructor
-    · intro h
-      rw [numeratorHom_apply, numeratorHom_apply, oreDiv_eq_iff] at h
-      rcases h with ⟨u, v, h₁, h₂⟩
-      dsimp at h₂
-      rw [one_mul, one_mul] at h₂
-      subst h₂
-      use u
-      simpa only [mul_comm] using h₁.symm
-    · rintro ⟨s, h⟩
-      rw [numeratorHom_apply, numeratorHom_apply, oreDiv_eq_iff]
-      refine' ⟨s, s, _, _⟩
-      · simpa [mul_comm] using h.symm
-      · simp [one_mul]
+  exists_of_eq r₁ r₂ := by
+    dsimp
+    intro h
+    rw [numeratorHom_apply, numeratorHom_apply, oreDiv_eq_iff] at h
+    rcases h with ⟨u, v, h₁, h₂⟩
+    dsimp at h₂
+    rw [one_mul, one_mul] at h₂
+    subst h₂
+    use u
+    simpa only [mul_comm] using h₁.symm
 #align ore_localization.localization_map OreLocalization.localizationMap
 
 /-- If `R` is commutative, Ore localization and monoid localization are isomorphic. -/

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

@@ -736,7 +736,8 @@ theorem right_distrib (x y z : R[S⁻¹]) : (x + y) * z = x * z + y * z := by
   rw [OreLocalization.expand' r₁ s₁ sa]
   rw [OreLocalization.expand r₂ s₂ ra (by rw [← ha]; apply SetLike.coe_mem)]
   rw [← Subtype.coe_eq_of_eq_mk ha]
-  repeat' rw [oreDiv_mul_oreDiv]; simp only [add_mul, add_oreDiv]
+  repeat rw [oreDiv_mul_oreDiv]
+  simp only [add_mul, add_oreDiv]
 #align ore_localization.right_distrib OreLocalization.right_distrib
 
 instance instSemiringOreLocalization : Semiring R[S⁻¹] :=

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

This has nice performance benefits.

@@ -44,7 +44,7 @@ open OreLocalization
 
 namespace OreLocalization
 
-variable (R : Type _) [Monoid R] (S : Submonoid R) [OreSet S]
+variable (R : Type*) [Monoid R] (S : Submonoid R) [OreSet S]
 
 /-- The setoid on `R × S` used for the Ore localization. -/
 def oreEqv : Setoid (R × S) where
@@ -71,7 +71,7 @@ def oreEqv : Setoid (R × S) where
 end OreLocalization
 
 /-- The ore localization of a monoid and a submonoid fulfilling the ore condition. -/
-def OreLocalization (R : Type _) [Monoid R] (S : Submonoid R) [OreSet S] :=
+def OreLocalization (R : Type*) [Monoid R] (S : Submonoid R) [OreSet S] :=
   Quotient (OreLocalization.oreEqv R S)
 #align ore_localization OreLocalization
 
@@ -79,7 +79,7 @@ namespace OreLocalization
 
 section Monoid
 
-variable {R : Type _} [Monoid R] {S : Submonoid R}
+variable {R : Type*} [Monoid R] {S : Submonoid R}
 
 variable (R S) [OreSet S]
 
@@ -144,7 +144,7 @@ protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t
 
 /-- A function or predicate over `R` and `S` can be lifted to `R[S⁻¹]` if it is invariant
 under expansion on the right. -/
-def liftExpand {C : Sort _} (P : R → S → C)
+def liftExpand {C : Sort*} (P : R → S → C)
     (hP : ∀ (r t : R) (s : S) (ht : (s : R) * t ∈ S), P r s = P (r * t) ⟨s * t, ht⟩) : R[S⁻¹] → C :=
   Quotient.lift (fun p : R × S => P p.1 p.2) fun (r₁, s₁) (r₂, s₂) ⟨u, v, hr₂, hs₂⟩ => by
     dsimp at *
@@ -158,7 +158,7 @@ def liftExpand {C : Sort _} (P : R → S → C)
 #align ore_localization.lift_expand OreLocalization.liftExpand
 
 @[simp]
-theorem liftExpand_of {C : Sort _} {P : R → S → C}
+theorem liftExpand_of {C : Sort*} {P : R → S → C}
     {hP : ∀ (r t : R) (s : S) (ht : (s : R) * t ∈ S), P r s = P (r * t) ⟨s * t, ht⟩} (r : R)
     (s : S) : liftExpand P hP (r /ₒ s) = P r s :=
   rfl
@@ -166,7 +166,7 @@ theorem liftExpand_of {C : Sort _} {P : R → S → C}
 
 /-- A version of `liftExpand` used to simultaneously lift functions with two arguments
 in `R[S⁻¹]`. -/
-def lift₂Expand {C : Sort _} (P : R → S → R → S → C)
+def lift₂Expand {C : Sort*} (P : R → S → R → S → C)
     (hP :
       ∀ (r₁ t₁ : R) (s₁ : S) (ht₁ : (s₁ : R) * t₁ ∈ S) (r₂ t₂ : R) (s₂ : S)
         (ht₂ : (s₂ : R) * t₂ ∈ S),
@@ -183,7 +183,7 @@ def lift₂Expand {C : Sort _} (P : R → S → R → S → C)
 #align ore_localization.lift₂_expand OreLocalization.lift₂Expand
 
 @[simp]
-theorem lift₂Expand_of {C : Sort _} {P : R → S → R → S → C}
+theorem lift₂Expand_of {C : Sort*} {P : R → S → R → S → C}
     {hP :
       ∀ (r₁ t₁ : R) (s₁ : S) (ht₁ : (s₁ : R) * t₁ ∈ S) (r₂ t₂ : R) (s₂ : S)
         (ht₂ : (s₂ : R) * t₂ ∈ S),
@@ -375,7 +375,7 @@ theorem numerator_isUnit (s : S) : IsUnit (numeratorHom (s : R) : R[S⁻¹]) :=
 
 section UMP
 
-variable {T : Type _} [Monoid T]
+variable {T : Type*} [Monoid T]
 
 variable (f : R →* T) (fS : S →* Units T)
 
@@ -436,7 +436,7 @@ end Monoid
 
 section CommMonoid
 
-variable {R : Type _} [CommMonoid R] {S : Submonoid R} [OreSet S]
+variable {R : Type*} [CommMonoid R] {S : Submonoid R} [OreSet S]
 
 theorem oreDiv_mul_oreDiv_comm {r₁ r₂ : R} {s₁ s₂ : S} :
     r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r₁ * r₂ /ₒ (s₁ * s₂) := by
@@ -489,7 +489,7 @@ end CommMonoid
 
 section Semiring
 
-variable {R : Type _} [Semiring R] {S : Submonoid R} [OreSet S]
+variable {R : Type*} [Semiring R] {S : Submonoid R} [OreSet S]
 
 private def add'' (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) : R[S⁻¹] :=
   (r₁ * oreDenom (s₁ : R) s₂ + r₂ * oreNum (s₁ : R) s₂) /ₒ (s₁ * oreDenom (s₁ : R) s₂)
@@ -749,7 +749,7 @@ instance instSemiringOreLocalization : Semiring R[S⁻¹] :=
 
 section UMP
 
-variable {T : Type _} [Semiring T]
+variable {T : Type*} [Semiring T]
 
 variable (f : R →+* T) (fS : S →* Units T)
 
@@ -827,7 +827,7 @@ end Semiring
 
 section Ring
 
-variable {R : Type _} [Ring R] {S : Submonoid R} [OreSet S]
+variable {R : Type*} [Ring R] {S : Submonoid R} [OreSet S]
 
 /-- Negation on the Ore localization is defined via negation on the numerator. -/
 protected def neg : R[S⁻¹] → R[S⁻¹] :=
@@ -878,7 +878,7 @@ open nonZeroDivisors
 
 open Classical
 
-variable {R : Type _} [Ring R] [Nontrivial R] [OreSet R⁰]
+variable {R : Type*} [Ring R] [Nontrivial R] [OreSet R⁰]
 
 instance nontrivial : Nontrivial R[R⁰⁻¹] :=
   nontrivial_of_nonZeroDivisors (refl R⁰)

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>

@@ -246,7 +246,7 @@ protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
     apply OreLocalization.expand
 #align ore_localization.mul OreLocalization.mul
 
-instance : Mul R[S⁻¹] :=
+instance instMulOreLocalization : Mul R[S⁻¹] :=
   ⟨OreLocalization.mul⟩
 
 theorem oreDiv_mul_oreDiv {r₁ r₂ : R} {s₁ s₂ : S} :
@@ -268,7 +268,7 @@ def oreDivMulChar' (r₁ r₂ : R) (s₁ s₂ : S) :
   ⟨oreNum r₂ s₁, oreDenom r₂ s₁, ore_eq r₂ s₁, oreDiv_mul_oreDiv⟩
 #align ore_localization.ore_div_mul_char' OreLocalization.oreDivMulChar'
 
-instance : One R[S⁻¹] :=
+instance instOneOreLocalization : One R[S⁻¹] :=
   ⟨1 /ₒ 1⟩
 
 protected theorem one_def : (1 : R[S⁻¹]) = 1 /ₒ 1 :=
@@ -316,7 +316,7 @@ protected theorem mul_assoc (x y z : R[S⁻¹]) : x * y * z = x * (y * z) := by
   rw [mul_assoc, hc, ← mul_assoc (b := ra), ← ha, mul_assoc]
 #align ore_localization.mul_assoc OreLocalization.mul_assoc
 
-instance : Monoid R[S⁻¹] :=
+instance instMonoidOreLocalization : Monoid R[S⁻¹] :=
   { OreLocalization.instMulOreLocalization,
     OreLocalization.instOneOreLocalization with
     one_mul := OreLocalization.one_mul
@@ -595,7 +595,7 @@ private def add : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] := fun x =>
       -- Porting note: `Quotient.mk'` required
       simp [(· /ₒ ·), Quotient.mk', Quotient.sound hyz])
 
-instance : Add R[S⁻¹] :=
+instance instAddOreLocalization : Add R[S⁻¹] :=
   ⟨add⟩
 
 theorem oreDiv_add_oreDiv {r r' : R} {s s' : S} :
@@ -679,8 +679,8 @@ protected theorem add_comm (x y : R[S⁻¹]) : x + y = y + x := by
   change add' _ _ (_ /ₒ _) = _; apply add'_comm
 #align ore_localization.add_comm OreLocalization.add_comm
 
-instance : AddCommMonoid R[S⁻¹] :=
-  { OreLocalization.instAddOreLocalizationToMonoidToMonoidWithZero with
+instance instAddCommMonoidOreLocalization : AddCommMonoid R[S⁻¹] :=
+  { OreLocalization.instAddOreLocalization with
     add_comm := OreLocalization.add_comm
     add_assoc := OreLocalization.add_assoc
     zero := zero
@@ -739,8 +739,8 @@ theorem right_distrib (x y z : R[S⁻¹]) : (x + y) * z = x * z + y * z := by
   repeat' rw [oreDiv_mul_oreDiv]; simp only [add_mul, add_oreDiv]
 #align ore_localization.right_distrib OreLocalization.right_distrib
 
-instance : Semiring R[S⁻¹] :=
-  { OreLocalization.instAddCommMonoidOreLocalizationToMonoidToMonoidWithZero,
+instance instSemiringOreLocalization : Semiring R[S⁻¹] :=
+  { OreLocalization.instAddCommMonoidOreLocalization,
     OreLocalization.instMonoidOreLocalization with
     zero_mul := OreLocalization.zero_mul
     mul_zero := OreLocalization.mul_zero
@@ -837,7 +837,7 @@ protected def neg : R[S⁻¹] → R[S⁻¹] :=
     rw [neg_mul_eq_neg_mul, ← OreLocalization.expand]
 #align ore_localization.neg OreLocalization.neg
 
-instance : Neg R[S⁻¹] :=
+instance instNegOreLocalization : Neg R[S⁻¹] :=
   ⟨OreLocalization.neg⟩
 
 @[simp]
@@ -850,8 +850,8 @@ protected theorem add_left_neg (x : R[S⁻¹]) : -x + x = 0 := by
 #align ore_localization.add_left_neg OreLocalization.add_left_neg
 
 instance ring : Ring R[S⁻¹] :=
-  { OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero,
-    OreLocalization.instNegOreLocalizationToMonoidToMonoidWithZeroToSemiring with
+  { OreLocalization.instSemiringOreLocalization,
+    OreLocalization.instNegOreLocalization with
     add_left_neg := OreLocalization.add_left_neg }
 
 open nonZeroDivisors

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Jakob von Raumer. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob von Raumer, Kevin Klinge
-
-! This file was ported from Lean 3 source module ring_theory.ore_localization.basic
-! leanprover-community/mathlib commit 861a26926586cd46ff80264d121cdb6fa0e35cc1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.MonoidLocalization
 import Mathlib.RingTheory.NonZeroDivisors
 import Mathlib.RingTheory.OreLocalization.OreSet
 import Mathlib.Tactic.NoncommRing
 
+#align_import ring_theory.ore_localization.basic from "leanprover-community/mathlib"@"861a26926586cd46ff80264d121cdb6fa0e35cc1"
+
 /-!
 
 # Localization over right Ore sets.

Changes are of the form

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

@@ -735,7 +735,7 @@ theorem right_distrib (x y z : R[S⁻¹]) : (x + y) * z = x * z + y * z := by
   induction' x using OreLocalization.ind with r₁ s₁
   induction' y using OreLocalization.ind with r₂ s₂
   induction' z using OreLocalization.ind with r₃ s₃
-  rcases oreDivAddChar' r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩; rw [ha']; clear ha'; norm_cast  at ha
+  rcases oreDivAddChar' r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩; rw [ha']; clear ha'; norm_cast at ha
   rw [OreLocalization.expand' r₁ s₁ sa]
   rw [OreLocalization.expand r₂ s₂ ra (by rw [← ha]; apply SetLike.coe_mem)]
   rw [← Subtype.coe_eq_of_eq_mk ha]
@@ -787,7 +787,7 @@ def universalHom : R[S⁻¹] →+* T :=
       congr 1
       rw [mul_assoc]
       congr 1
-      norm_cast  at h₃
+      norm_cast at h₃
       have h₃' := Subtype.coe_eq_of_eq_mk h₃
       rw [← Units.val_mul, ← mul_inv_rev, ← fS.map_mul, h₃']
       have hs₂r₃ : ↑s₂ * r₃ ∈ S := by

I wrote a script to find lines that contain an odd number of backticks

@@ -168,7 +168,7 @@ theorem liftExpand_of {C : Sort _} {P : R → S → C}
 #align ore_localization.lift_expand_of OreLocalization.liftExpand_of
 
 /-- A version of `liftExpand` used to simultaneously lift functions with two arguments
-in ``R[S⁻¹]`.-/
+in `R[S⁻¹]`. -/
 def lift₂Expand {C : Sort _} (P : R → S → R → S → C)
     (hP :
       ∀ (r₁ t₁ : R) (s₁ : S) (ht₁ : (s₁ : R) * t₁ ∈ S) (r₂ t₂ : R) (s₂ : S)

Part 3 of #5001

@@ -122,7 +122,7 @@ protected theorem expand (r : R) (s : S) (t : R) (hst : (s : R) * t ∈ S) :
   refine' ⟨s, t * s, _, _⟩ <;> dsimp <;> rw [mul_assoc]
 #align ore_localization.expand OreLocalization.expand
 
-/-- A fraction is equal to its expansion by an factor from s. -/
+/-- A fraction is equal to its expansion by a factor from s. -/
 protected theorem expand' (r : R) (s s' : S) : r /ₒ s = r * s' /ₒ (s * s') :=
   OreLocalization.expand r s s' (by norm_cast; apply SetLike.coe_mem)
 #align ore_localization.expand' OreLocalization.expand'

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

@@ -111,7 +111,7 @@ protected theorem ind {β : R[S⁻¹] → Prop} (c : ∀ (r : R) (s : S), β (r
 #align ore_localization.ind OreLocalization.ind
 
 theorem oreDiv_eq_iff {r₁ r₂ : R} {s₁ s₂ : S} :
-    r₁ /ₒ s₁ = r₂ /ₒ s₂ ↔ ∃ (u : S)(v : R), r₂ * u = r₁ * v ∧ (s₂ : R) * u = s₁ * v :=
+    r₁ /ₒ s₁ = r₂ /ₒ s₂ ↔ ∃ (u : S) (v : R), r₂ * u = r₁ * v ∧ (s₂ : R) * u = s₁ * v :=
   Quotient.eq''
 #align ore_localization.ore_div_eq_iff OreLocalization.oreDiv_eq_iff
 

These are all doc fixes

@@ -26,7 +26,7 @@ localization at `R - {0}` results in a division ring.
 ## Notations
 
 Introduces the notation `R[S⁻¹]` for the Ore localization of a monoid `R` at a right Ore
-subset `S`. Also defines a new heterogeneos division notation `r /ₒ s` for a numerator `r : R` and
+subset `S`. Also defines a new heterogeneous division notation `r /ₒ s` for a numerator `r : R` and
 a denominator `s : S`.
 
 ## References

This aims to be a faithful implementation of mathlib3's noncomm_ring tactic.

@@ -11,6 +11,7 @@ Authors: Jakob von Raumer, Kevin Klinge
 import Mathlib.GroupTheory.MonoidLocalization
 import Mathlib.RingTheory.NonZeroDivisors
 import Mathlib.RingTheory.OreLocalization.OreSet
+import Mathlib.Tactic.NoncommRing
 
 /-!
 
@@ -521,11 +522,11 @@ private theorem add''_char (r₁ : R) (s₁ : S) (r₂ : R) (s₂ : S) (rb : R)
   use sc * sd
   use rc * sd
   constructor <;> simp only [Submonoid.coe_mul]
-  · simp only [right_distrib, mul_assoc]
+  · noncomm_ring
     rw [← mul_assoc (a := rb), hd, ← mul_assoc (a := (sa : R)), hc]
-    simp only [mul_assoc]
+    noncomm_ring
   · rw [mul_assoc (a := (s₁ : R)), ← mul_assoc (a := (sa : R)), hc]
-    simp only [mul_assoc]
+    noncomm_ring
 
 attribute [local instance] OreLocalization.oreEqv
 

As reported on Zulip.

@@ -85,9 +85,9 @@ variable {R : Type _} [Monoid R] {S : Submonoid R}
 
 variable (R S) [OreSet S]
 
--- mathport name: «expr [ ⁻¹]»
 @[inherit_doc OreLocalization]
-notation:1075 R "[" S "⁻¹]" => OreLocalization R S
+scoped syntax:1075 term noWs atomic("[" term "⁻¹" noWs "]") : term
+macro_rules | `($R[$S⁻¹]) => ``(OreLocalization $R $S)
 
 attribute [local instance] oreEqv
 

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".

@@ -226,18 +226,15 @@ protected def mul : R[S⁻¹] → R[S⁻¹] → R[S⁻¹] :=
     dsimp at h₂
     rcases oreCondition r (s₂' * s_star) with ⟨p_flat, s_flat, h₃⟩
     simp only [S.coe_mul] at h₃
-    have : r₁ * r * s_flat = s₂ * p * (p' * p_flat) :=
-      by
+    have : r₁ * r * s_flat = s₂ * p * (p' * p_flat) := by
       rw [← mul_assoc, ← h₂, ← h₁, mul_assoc, h₃]
       simp only [mul_assoc]
     rw [mul'_char (r₂ * p) (r₁ * r) ⟨↑s₂ * p, hp⟩ ⟨↑s₁ * r, hr⟩ _ _ this]
     clear this
-    have hsssp : ↑s₁ * ↑s₂' * ↑s_star * p_flat ∈ S :=
-      by
+    have hsssp : ↑s₁ * ↑s₂' * ↑s_star * p_flat ∈ S := by
       rw [mul_assoc, mul_assoc, ← mul_assoc (s₂' : R), ← h₃, ← mul_assoc]
       exact S.mul_mem hr (SetLike.coe_mem s_flat)
-    have : (⟨↑s₁ * r, hr⟩ : S) * s_flat = ⟨s₁ * s₂' * s_star * p_flat, hsssp⟩ :=
-      by
+    have : (⟨↑s₁ * r, hr⟩ : S) * s_flat = ⟨s₁ * s₂' * s_star * p_flat, hsssp⟩ := by
       ext
       simp only [Submonoid.coe_mul]
       rw [mul_assoc, h₃, ← mul_assoc, ← mul_assoc]
@@ -713,8 +710,7 @@ protected theorem left_distrib (x y z : R[S⁻¹]) : x * (y + z) = x * y + x * z
   rcases oreDivMulChar' r₁ (r₂ * sa) s₁ (s₂ * sa) with ⟨rb, sb, hb, q⟩
   rw [q]
   clear q
-  have hs₃rasb : ↑s₃ * (ra * sb) ∈ S :=
-    by
+  have hs₃rasb : ↑s₃ * (ra * sb) ∈ S := by
     rw [← mul_assoc, ← ha]
     norm_cast
     apply SetLike.coe_mem

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.)

@@ -142,7 +142,6 @@ protected theorem eq_of_num_factor_eq {r r' r₁ r₂ : R} {s t : S} (h : r * t
     _ = r₁ * r' * (r₂ * t') /ₒ (s * t') := by rw [hr₂]
     _ = r₁ * r' * r₂ * t' /ₒ (s * t') := by simp [← mul_assoc]
     _ = r₁ * r' * r₂ /ₒ s := (OreLocalization.expand _ _ _ _).symm
-
 #align ore_localization.eq_of_num_factor_eq OreLocalization.eq_of_num_factor_eq
 
 /-- A function or predicate over `R` and `S` can be lifted to `R[S⁻¹]` if it is invariant

@@ -856,7 +856,7 @@ protected theorem add_left_neg (x : R[S⁻¹]) : -x + x = 0 := by
   induction' x using OreLocalization.ind with r s; simp
 #align ore_localization.add_left_neg OreLocalization.add_left_neg
 
-instance : Ring R[S⁻¹] :=
+instance ring : Ring R[S⁻¹] :=
   { OreLocalization.instSemiringOreLocalizationToMonoidToMonoidWithZero,
     OreLocalization.instNegOreLocalizationToMonoidToMonoidWithZeroToSemiring with
     add_left_neg := OreLocalization.add_left_neg }
@@ -868,7 +868,7 @@ theorem numeratorHom_inj (hS : S ≤ R⁰) : Function.Injective (numeratorHom :
   rw [numeratorHom_apply, numeratorHom_apply, oreDiv_eq_iff] at h
   rcases h with ⟨u, v, h₁, h₂⟩
   simp only [S.coe_one, one_mul] at h₂
-  rwa [← h₂, mul_cancel_right_mem_non_zero_divisor (hS (SetLike.coe_mem u)), eq_comm] at h₁
+  rwa [← h₂, mul_cancel_right_mem_nonZeroDivisors (hS (SetLike.coe_mem u)), eq_comm] at h₁
 #align ore_localization.numerator_hom_inj OreLocalization.numeratorHom_inj
 
 theorem nontrivial_of_nonZeroDivisors [Nontrivial R] (hS : S ≤ R⁰) : Nontrivial R[S⁻¹] :=
@@ -887,7 +887,7 @@ open Classical
 
 variable {R : Type _} [Ring R] [Nontrivial R] [OreSet R⁰]
 
-instance : Nontrivial R[R⁰⁻¹] :=
+instance nontrivial : Nontrivial R[R⁰⁻¹] :=
   nontrivial_of_nonZeroDivisors (refl R⁰)
 
 variable [NoZeroDivisors R]
@@ -911,7 +911,7 @@ protected def inv : R[R⁰⁻¹] → R[R⁰⁻¹] :=
           apply OreLocalization.expand)
 #align ore_localization.inv OreLocalization.inv
 
-instance : Inv R[R⁰⁻¹] :=
+instance inv' : Inv R[R⁰⁻¹] :=
   ⟨OreLocalization.inv⟩
 
 protected theorem inv_def {r : R} {s : R⁰} :
@@ -937,10 +937,10 @@ protected theorem inv_zero : (0 : R[R⁰⁻¹])⁻¹ = 0 := by
   simp
 #align ore_localization.inv_zero OreLocalization.inv_zero
 
-instance : DivisionRing R[R⁰⁻¹] :=
-  { OreLocalization.instNontrivialOreLocalizationToMonoidToMonoidWithZeroToSemiringNonZeroDivisors,
-    OreLocalization.instInvOreLocalizationToMonoidToMonoidWithZeroToSemiringNonZeroDivisors,
-    OreLocalization.instRingOreLocalizationToMonoidToMonoidWithZeroToSemiring with
+instance divisionRing : DivisionRing R[R⁰⁻¹] :=
+  { OreLocalization.nontrivial,
+    OreLocalization.inv',
+    OreLocalization.ring with
     mul_inv_cancel := OreLocalization.mul_inv_cancel
     inv_zero := OreLocalization.inv_zero }
 

The proofs in mathlib use noncomm_ring and assoc_rw.

Co-authored-by: Komyyy <pol_tta@outlook.jp>